I think a 2D engine might be better than 3D in some regards. The level editor (if it existed) would be far more accessible than one for a 3D game, and that was certainly a big part of JJ2's longevity. Give it unlimited layers and the ability to scale/colour layers and you've already got something pretty good.
I'm not really one to talk about what made the Jazz games popular when they were first released. I haven't been around long enough for that. Thinking about it today, though, if it were to be done it would most likely be banking hugely on nostalgia. Plenty of companies have been having a go at rebooting their old 2D franchises in HD, so if Epic were to do the same with Jazz I'd expect it to be built off of entirely different design goals than the original games.