In that case.
IN FAIRNESS: I have seen How to Train Your Dragon at least 30 times, and most recently about a year ago. I have seen Toy Story 3 twice, most recently probably 4-5 years ago, and I didn't get all the way through my second watch.
I will be judging these two films as works of cinematic art. Specifically I will compare their use of the following:
* Visual storytelling
* Musical score
* Writing and characterization
To determine which of the two films (How to Train Your Dragon, hands down) is a "better" work of animated cinema. This is not to say that others may prefer the other (Toy Story 3, inferior, hands down) for a variety of reasons; but that the former is from an artistic perspective a more thoroughly polished and successful product.
...Let's just say there's a REASON I can watch HTTYD 30 times and not get bored of it, yeah?
How to Train Your Dragon excels at visual storytelling. Because the majority of the film focuses on a relationship between a human and an animal, the film BY NECESSITY must tell a not-insignificant portion of its story without dialogue. Three sequences in the film stand out as being excellent examples. The most famous being, of course, the "forbidden friendship" sequence in which Hiccup discovers the downed and injured Toothless and slowly, carefully, makes first contact with him. This is also the moment that teenage me fell in love with this movie in theaters, and it had such a poignant effect on me that I still remember exactly how it felt to experience it for the first time. I'll let this "speak" for itself, without words:
[I've timestamped it appropriately.]
...ok I just watched the whole thing again and started crying again but now I've somewhat composed myself and can continue. This sequence is not only aesthetically pleasing to watch (the colors changing as the sun sets, the gorgeous music track); it communicates SO MUCH without words. It establishes the bond between the two most prominent characters in the film without so much as a word, more powerfully than dialogue COULD have done. It reveals Hiccup's isolation and desperation and curiosity, it reveals Toothless's playful yet wild nature; it defines a moment of connection that changes Hiccup's entire worldview and sets the entire plot of the movie rolling. After Hiccup's initial musing about Toothless's lack of teeth, he voices no further musings or dialogue, but his thoughts are SO CLEARLY communicated by his incredibly emotive expressions and by the context of what is happening.
My other favorite example of this in HTTYD is the "see you tomorrow" sequence, in which we see Hiccup alternating between hanging out with Toothless, trying to repair his tail, and in the meanwhile learning more about dragons; then applying what he learns to get by in Dragon Training without violence.
This sequence does have some dialogue where the absence thereof would be awkward (when Hiccup is with his peers), but the dialogue is background to the visuals and the music that are primarily telling the story. This sequence excellently communicates Hiccup's growing popularity, Astrid's growing resentment, the development of Toothless and Hiccup's ability to fly together despite Toothless's injury, and Hiccup's sense of living a blatant lie as he grows more attached to dragons and more critical of the Vikings' violent treatment of them. It sets up all of the central conflicts: Hiccup vs. the Vikings, Hiccup vs. Astrid, Astrid/Vikings vs. Dragons, and BELIEVABLY develops them to a breaking point, in a way that feels very natural and is also just pleasing to watch. It's a really entertaining segment.
My other favorite scene in this category - I am basically going over the majority of the film at this point, but that's because the majority of the film does NOT rely on dialogue to tell its story, and because the majority of the film is ABSOLUTELY STUNNING and worth mentionign here - is the "Test Drive" scene where Hiccup and Toothless first truly, successfully, freely fly together.
This is the only scene I have ever witnessed in cinema that makes its audience feel the thrill of flight. The musical score, the sounds of rushing winds, the camera work; you can almost feel the wind rushing past you while you ride along with Hiccup and Toothless. The little cheat sheet at the beginning is also a nice nod to Hiccup's artistry and craftsmanship, but that was already pretty well established before; a nice touch nonetheless.
It's far from the most important scene plot-wise in the movie, but it very powerfully and artfully conveys the FEELING of freedom that Hiccup and Toothless have been yearning for the entire movie; it is, in my opinion, the best possible argument for the audience that what Hiccup and Toothless have is worth fighting for: allowing the audience to feel the same joy along with them.
If you're feeling pedantic you might point out that there is dialogue when they're both falling but it feels natural for Hiccup's character, and furthermore, my focus is on the majority of this sequence that does NOT feature dialogue, merely visuals and audio.
I won't link it because I've already linked enough dragon scenes... actually yes I will. Romantic Flight is the last essential segment of pure visual storytelling in this movie as far as I am concerned:
GOD, THIS SCENE IS STUNNING. IT'S GORGEOUS. I'M GETTING SHIVERS ALL **** OVER AGAIN. Like with Test Drive, this scene is what resolves the Hiccup vs. Astrid / Astrid vs. Dragons central conflict, and it requires no words to do so. You watch Astrid completely change her mind and perspective toward dragons, you watch her body language loosen up, you watch her expression turn to wonder, and you watch Toothless get lost in the clouds in one of the most gorgeous flight scenes I've ever seen in my **** life. There is no good verbal argument to change Astrid's mind about dragons but this scene shows her coming to terms with a new reality, with no words, in a very believable and heartfelt way. (Again, there are words at the beginning, but the real MEAT of the scene is silent and without dialogue.)
Toy Story 3's notable moment here is gonna get mentioned below in color/aesthetics. You know the scene.
Luckily most of the scenes I linked above pretty succinctly give my argument on this front for HTTYD. The gradual sunset in the Forbidden Friendship scene; the BREATHTAKING colors of the Romantic Flight scene.... those palettes are just absolutely incredible. Beyond use of color, though, I also find that How to Train Your Dragon's visual style overall is more appealing. Every member of the main cast (and every dragon) has a very distinct silhouette that informs their character/personality. The world feels very vibrant and diverse.
Toy Story 3 gets some credit here because for all that I don't remember about that movie, I vividly recall that dramatic 'we gon die' scene at the end that we all cried at, and the INTENSE RED was an incredible mood setter and really made the audience feel the incinerating heat. That was an intense scene. Linking in fairness:
It is also, unfortunately, the only visually remarkable scene that I remember from the movie. As for overall visual design, the toys all have varied designs but I can't really give this movie credit for them because it's a threequel-that-no-one-asked-for, and because the human characters and surrounding world all still look exactly like they could be in any 3D animated Disney movie ever. Disney's stuck in this "animated but everyone still needs to look almost realistic but not quite" rut and seemingly refuses to be more free with its visual style. The neighborhood is just cookie cutter "animated suburbia" and virtually nothing about the world feels particularly interesting or vibrant. Up is a much better example of what Disney/Pixar can do in this department (although I found Up also fell flat on a re-watch), but Up is not the movie that defeated HTTYD for an Oscar, so who cares. IN FAIRNESS, Toy Story is not set in a distinct or special world or anything, the whole POINT is it happens in suburbia from a toy's perspective; that said so much of the world is left to assumptions based on the audience's experience of the real world that the movie itself does none of the heavy lifting here. How to Train Your Dragon established and fleshed out an entire world where Toy Story 3 just assumes you already know about day cares and stuff.
Listen to the entire HTTYD soundtrack and then listen to the Toy Story 3 soundtrack and tell me that they even **** compare lol. Even just in the scenes I linked, HTTYD's soundtrack is memorable and has so much character; Toy Story's is kind of just background atmosphere and dramatic DUN-DUNs and little more. Moreover, HTTYD's defines leitmotifs during its early visual/musical segments that inform the audience's reaction to later events when they're brought back in a new context.
I mentioned character design earlier, but the designs come to LIFE so much more convincingly in HTTYD.
The animators animating Hiccup actually based many of his movements, quirks, and expressions on his voice actor because he was so emotive during recording. Hiccup FEELS ALIVE. They studied movements of panthers and other animals and based Toothless's movements off of them, and you can tell because he acts like a real, living animal. Just watch all of the segments I linked above; it's not just in the detail of the models (this was almost 10 years ago and it still looks REALLY good) but in HOW they move. The ruffle of Hiccup's hair as Toothless breathes out behind him at the end of Forbidden Friendship. The physics behind how everything moves in the air during the flight sequences. The facial expressions accompanying all of the dialogue. The DIFFERENT KINDS OF FIRE each dragon spits out. Little movement tics that inform the characters' internal thought processes. I've said it before and I cannot stress enough: This Movie Feels Alive.
Toy Story 3 does not particularly stand out to me in this regard. The characters emote but don't have the same details in their movements that convince me that they are PEOPLE rather than symbols. In the above clip, the expressions are believable, the motions convey the characters' feelings, but there is nothing akin to just Hiccup's face during the entire Forbidden Friendship scene. "Brave" is a SIGNIFICANTLY better example of what Disney/Pixar can do as far as lively animation goes, but again, it didn't beat HTTYD for an Oscar, so who cares.
The depth of animation is what makes HTTYD infinitely rewatchable to me. It is a damn work of art.
WRITING AND CHARACTERIZATION
First of all, I'm just gonna say that Toy Story 3 suffers from having the exact same writing as every Pixar flick ever, which made it a really powerful experience the first time and kind of boring the second time. From my personal experience the vast majority of Pixar blockbusters are not really rewatchable because they all have the same villain plot twist, and when virtually the entire movie is setting up for that dramatic villain plot twist reveal, it makes it hard to watch all the crap it takes to finally get to the point. And again, the characters feel more like symbols or ideas than people, so when you already know what they communicate/represent there's not much more for them to do.
How to Train Your Dragon, on the other hand, as I have said thousands of times before and will continue to say until I die, FEELS ALIVE. There are clever snippets of dialogue in the background you don't hear until a second or third watch. There are intentional callbacks ("I did this" - Hiccup, when he first injures Toothless; later repeated by Stoick when he believes Hiccup to be dead. And the "you just gestured to all of me" which is played for laughs at first and heartwarming at the end). And the story doesn't rely on a dramatic plot twist of who the Real Bad Guy Was All Along because its central conflicts are about a boy and his dad, a culture interacting with the world around them, and dealing with not fitting in and not feeling heard. HTTYD's dialogue is witty and its writing is solid and the story it has to tell has depth to it that makes it worth watching again and again to see all of the different ways its ideas are hinted at and fleshed out.
How to Train Your Dragon was an excellent and artful movie. Toy Story 3 was a nostalgic opportunity flick because all the hashtag nineties kids were going off to college and everyone was emotional about it. There isn't even a comparison imo and I'll be mad about this until the day I die.