Can a Spider-Man film "reach the level of depth and complexity of The Dark Knight?" That's an unfair question.
To start, the two comic book companies have always had two very different approaches and it shows on film. When I think of DC Comics, I think of psychological engagement. When I think of Marvel Comics, I think of contemporary appeal, what people want in the here and now. Neither approach is necessarily bad in the transition to film. Sometimes I want films that are competent yet spectacular. Other times, I'm willing to put aside the popcorn and be challenged to think. It's hard to compare and contrast once I've realized I have differing sets of expectations.
When you examine both characters in their film franchises, it's easy to tell how that difference in tone impacts them. Batman delves into a lot of symbolism, whereas Spider-Man is the Everyman. We've seen what happens when Batman tries to be an Everyman figure; it gets goofy, because we know his background doesn't allow for a constant stream of feelgood moments. Similarly, the last Spider-Man film's direction clashed with what could have been a dark, pessimistic story and we got what we got: this odd amalgam of the family friendly with the potentially nightmarish. In neither scenario do the characters hold up, but that's not because they've somehow gone bad or are incapable of greatness. The tone's just wonky.
The goal of the next Spider-Man film should be to give people a fresh, appealing story. Its goal should not be to "top" The Dark Knight. You don't excel by setting for the same bar. You excel by being a good kind of different. So long as they have a good sense of what people want to see and work with the tone they can do the most with, any Spider-Man sequel can be worthy of praise. Granted, different direction could be in order, but Raimi's done well in the past. They can safely move forward, if that's what Sony's still intent on doing with this film franchise.
