Here's an old post I made on the subject,
While analog controls would be nice for turning, that's not my main gripe with gamepad controls in FPS in general. I also didn't say that you can't do some things, but you can't do them easily or quickly enough to be as competitive as you can with keyboard or mouse + keyboard (NOT plain mouse, which has a lot of limitations). My main complaints are that, with a gamepad:
Like it or not, a gamepad is not the optimal control for a fast-paced FPS, also due to human physiology/ergonomic reasons. All the above together result in a clumsy control scheme, which introduces a handicap to playing, which no amount of training can remove. It's not enough to map every possible control on the gamepad, it must also be ergonomically usable and competitive with other control schemes, I cannot stress that enough. If I have to become a contorsionist to master a controller, then I'll pass.
- One of the most important controls in Doom (direction) is crammed on the small D-pad which you can only control with your left hand's thumb, which is usually not the good one for most of the population (right handed). At least in pure keyboard vanilla controls, this is on your right hand, and spread between 3 fingers, not just one.
- Switching between turning and strafing is slow and clumsy, mainly because the strafe key is under rather than near the fire key by default (but this might be configurable)
- The shoulder pads for strafing are nearly impossible to coordinate, and cannot be used at the same time with the gamepad, as e.g. strafe modifiers.
I don't know how the PSX mouse is supposed to operate with Final Doom, but unless you can combine it with WASD-like controls, it'll be probably an even worse handicap (like playing PC Doom with pure mouse controls, where you have to press a mouse button to walk).
Of course, handicap is relative to the best known control scheme for a FPS, which is, of course, WASD + mouse, until someone proves otherwise by trashing (or even just matching) an equally-skilled rival in DM using nothing but a gamepad.
Let's ask it to you straight: could a gamepad user even hope to beat a keyboarder in a DM, at skill level parity? And even if the gamepadder is the top of the top in his league, could he ever compete with the top of the top keyboarder or mouse + WASDer? Playing Doom with anythin other than mouse + WASD is a handicap, and the fact that none risks using anything else in DM is a testament to how good a control scheme it is. And since human opponents are much harder to kill than monsters, the above also applies to single player.
The above being said, I reiterate my proposal/challenge for organizing a "keyboarders DM league" and a "gamepadders DM league", and have the best of either team being pitted against barely average WASD+mouse DMers. Guess where I'd put my money ;-)