The Jack and Rose aspect is probably what has aged the most, however, the ship itself and the actual sinking are still fantastic. I think what the movie does really well is the introduction in Southampton, the attention to detail of the inside of the ship, and pretty much the entire last hour or so. The Nearer My God to Thee sequence still packs a wallop. First it's the melancholy of the hymn over the brief looks in on folks like Andrews and the Strausses, and then it's a juxtaposition over the chaos and fear on the deck.* I also liked the way Cameron would show some lingering, almost romantic, shots of aspects of the ship being destroyed and also some sudden and violent ones. The image of the main ceiling bursting and flooding while some of the folks inside are screaming is haunting. Really, all of the destruction is haunting in some way. It was also smart to look in on the life boats and see their perspective from the outside. And because Kathy Bates is a treasure and deserves as much screen time as possible. And speaking of life boats, when the one does go back and you not only see the bodies frozen but the abject guilt on the face of the crew member when he realizes "We waited too long" it's so well done. I understand some of the criticisms of the movie, but it's so much more than star crossed lovers and I still think it's worth it.
And if you wanna play the game of did it deserve all those Oscars? It mostly won in technical or artistic categories (Sound, cinematography, art direction, score, costumes, etc. And the damn song won too.) and I think it's hard to argue against those. (maybe the damn song, but there's no way that wasn't going to win.) Also, as the mastermind of all of that, it's hard to say Cameron didn't deserve his Oscar for direction as well. His attention to detail is crazy. Best picture? In retrospect from 20 plus years out, the other nominee that maybe coulda/shoulda/woulda is LA Confidential but it's not as if LA Confidential has become this zeigeisty classic and Titanic this afterthought. (The other nominees were As Good as It Gets, the Full Monty, and Good Will Hunting.) Anything can be debated but Titanic winning doesn't feel like a whiff to me even in hindsight.
*Whenever I need a knife, I like to say "I need a knife! I need a knife!" all panicked and English accent like the crew member. It's even better when people don't get the reference and have no clue what I'm doing.