Since i'm working on what i suppose it's a 2.5D game i thought i could give my very honest opinion. In my game everything it's 3d except that since it's a space shooter and camera angle is fixed i work out all the collision and "physics" in 2D because it saves a LOT of computation time even though i have to "manually" project the points.
I still think that Trine & Trine 2 ( great games btw ) are another interpretation of 2.5D and Sacred ( if i remember correctly ) is isometric but with 3d models and i personally consider it 2.5D.
Doom... i wouldn't consider it 2.5D it's neither 3D nor 2.5D. I would put it in the Raycasting/fake 3D category.
Difference between 2.5 and 3d is that in 2.5 there is a side of a 3d model that is never view able due to control of the camera angles. Since this side is never viewable, it doesn't need to exist, so they can display a 3d model with some of it missing and you never can tell, this is a big optimization.
With the resources saved they can either add more detail to the view able sides, or not and keep the hardware requirements for the end user lower.
Of course it depends on the game, but for some 2.5D games if a part of the model is "missing" it can be gamebreaking for performance.
Just my two cents, please correct me if anything is wrong.