It's a completely different game. Street Fighter titles are, for the most part, 2D fighting games - as in, they fight on a single plane; you can only move up (jump), back and forward. Games like Virtua Fighter, Soul Calibur, and Dead or Alive, however, are 3D fighting games, as in, they let you move in several (8 I think) directions, so you can actually move around the environment. It greatly changes the gameplay and pacing of the title, as you can actually dodge, predict movement and attack in a different direction, etc. 2D fighters and 3D fighters are two totally different beasts. If you don't like one, you might like the other. If you're into Soul Calibur, Virtua Fighter, or any other 3D fighting title, I'd look into it.
That and the fighting game engine is completely different. Street Fighter is flashy, and has over the top special moves. Dead or Alive is more about combo's and movement.
Mechanically, the titles are vastly different. SSFIV3D and Dead or Alive: Dimensions do offer similar game play modes, though - Arcade, Online, SpotPass (simulation battles), training mode, etc.
Edit
Yeah, DoA titles, including the one for the 3DS, have interact-able environments. You can break objects by kicking people into them, flip off of them, etc. Hell, in the Other M stage, you can knock people into Ridley!