Titanic, for a few reasons:
1. It wasn't tied to a crass commercial gimmick that added nothing to the story and simply led to physical discomfort for many viewers.
2. It didn't take a political stand that bashed the viewers over the head with its obviousness every two minutes.
3. The love story, despite its awkwardness, worked better. Even though the Avatar romance developed more naturally -- over the course of weeks and months rather than just one or two nights in the case of Jack and Rose -- I found the characters in Titanic were simply more interesting and easier to relate to. It's possible this can be attributed to the uncanny valley effect of the CG and the fact it's slightly easier to relate to characters when your eyes aren't watering every few minutes and you're not being distracted by the 3-D smoke and mirrors.
4. Despite its length, I didn't want Titanic to end the first time I saw it. Avatar had me checking my watch after the first 2 hours.
5. Titanic had David Warner. Avatar simply didn't have any heavies of equal weight. When the "Angry American Colonel" (tm) got offed in Avatar, I was more of the opinion of "thank god he's gone" rather than any sort of "Yeah!" Fist-pumping moment. Not that I had that with Warner's character either, but at least I enjoyed his heavy.
6. Titanic didn't magically bring Jack back to life, or come up with a plot contrivance to keep him from being killed off. Cameron made the tough decision and stuck with it. Had the lead character in Avatar been allowed to be killed off, it would have actually increased my appreciation for the film. But of course Cameron wanted sequels, so he had to bring the guy back.
7. Titanic reaffirmed the value of human life. Avatar spent most of its running time working to convince the audience that humans are scum.
I could go on, but I'll hold at lucky 7. Since we're discussing the films' merits, I'll defer point #8 which would have been referencing the destructive impact the 3-D bandwagoning sparked by Avatar will have on the art of filmmaking and TV production and the further disenfranchisement of large segments of the audience. And point #9 about how having a big hit movie suddenly appears to have given James Cameron airs that he's some sort of political power now (this one means more to people here in Canada who've been watching the Cameron vs. the Oilsands saga).
Alex