Prince of Egypt has a lot going for it, and I mean a lot. It had a fantastic soundtrack, its storytelling was top-notch, the animation was some of the best Disney would ever put forth, the songs and the dramatic cinematic composition... Okay, let's compare to the rest of the Disney Renaissance.
Little Mermaid: Never saw it. No comment.
The Rescuers Down Under: Saw it when I was 5, don't remember a lick of it.
Beauty and the Beast: Saw it, owned it on pillow-case VHS, it was my reward for being a good boy. "Tale As Old As Time" gets my eyes cloudy some 20 years later. Gaston is a perfectly hateable douchebag, the romance was well-paced as believable... tough competition, even without my nostalgia-tinted glasses.
Aladdin: It had Robin Williams and Jafar, the follow-up TV cartoon was done better than it had any right to be, and the sequels were really good too. Again, tough competition.
The Lion King: Hoo boy. Can any opening number even hope to beat "Circle of Life"? Personal nostalgia aside, it's not as heavy a contender as some of the other ones.
Pocahontas: Trash. Had some nice art direction with Colors of the wind. NEXT.
The Hunchback of Notre Dame: Oh sweet Jesus, Frollo. I can't think of a more villainous character. In Quasimodo I can't think of a more tragic hero. If it weren't for the silly gargoyles, it could have been the Disney 2D magnum opus. Hellfire has to be, without question, the best villain song in the entire Disney song library. Friends On the Other Side is a close second.
Hercules: Lots of energy, fast-paced storytelling, nice stylized animation. All-around really good movie, but not quite great.
Mulan: Let's get down to business! To defeat... the Huns!!! Yeah, let's not kid ourselves here, that was the best part of the movie.
Tarzan: Blah. A great whacking lot of blah.
So, where does that leave us? Okay, so OP mentions "adult themes" but Hunchback has some heavily implied themes of sexual molestation and Esmeralda being a woman of loose morals, and Ursula's body language speaks awfully loudly of Ariel using her figure to attract Prince Eric; don't even get me stahted on Nala's "come hither" face in Lion King's Can You Feel the Love Tonight? sequence.
But of course, adult themes do not always a magnificent movie make; no, no, it's all in how the movie complements those themes, and that's where all the front-runners in this hypothetical footrace shine. Yes, Prince of Egypt is among them, so bear with me.
Beauty and the Beast shows use the moderately "adult" theme of how romance can blossom between unlikely people, if only a little consideration - Beast giving Belle a nice room and eventually showing her the library out of a desire to please her - and care - Belle being patient and caring for her big strong protector long enough to see the nice guy underneath the rough exterior - could be put into the relationship. Even if it's wrapped in a fairy tale ending, it's still one of the best, most satisfying romance stories I have ever seen.
Prince of Egypt gives us a raw, real rivalry between two people who are as good as siblings, irreparably separated by what they each see as their sworn duty to the power of their choosing: Ramses to his lineage, and Moses to his people and God. Both are sorrowful for the enmity, both are unfailingly resolute that they are right, for good or for ill. No rendition of the Book of Exodus has ever painted these main characters in such human light.
Hunchback. Oh, jeepers. Frollo believes that everything he says and does is right, and therefore, everything he says and does is right. Esmeralda, the morally "loose" character of the story, is the only one who can see what is truly right in the moment, including rescuing Quasimodo from the hysterical mob and befriending him. Phoebus serves as the bridge between the self-righteous Frollo and the morally-if-not-conventionally-good Esmeralda; strangely, this makes Phoebus' "knight in shining armor" status just a little more relatable, since he does the right thing by simply disobeying the unjust authority figure and later rallying the people to a just cause. And can we talk about the music again? Because it's literally the best.
Okay, I have my verdict. Beauty and the Beast will always be an unassailable classic, no doubt about that, but it can't hold up to Prince or Hunchback in my mind.
Prince of Egypt has a rock-solid theme, its story is told with terrific gravitas, and the cinematic ingenuity is fantastic.
The Hunchback of Notre Dame, on the other hand, rises above even Prince, because of one critical factor: Even its songs drove the narrative forward. Every note of every song lent weight to a character's struggles, hopes, and dreams; yes, even that silly A Guy Like You song; it reinforced Quasimodo's self-worth enough that he could finally stand up to Frollo for the sake of his one real friend, Esmeralda, whom he respected enough as a person to recognize she was happier with Phoebus. And, again, Hellfire.
So... no. You're awfully close, but I have to disagree, Hunchback was the best movie to come out of the Disney Renaissance, by a hair.