DS4 d-pad elitist here, too. If you’re willing to spend $50 on a controller, you should absolutely spend about $10 more and just get a DS4.
Yes, for fighting games specifically, a Saturn pad or a Hori pad specifically designed for fighting games might be better for performing circular motions. But that has to be the only advantage the d-pads of those controllers have–and in that case, just use an arcade stick, there’s absolutely no comparison to a d-pad anyway when it comes to fighting games. One of the world’s top SF players uses a measly PSX controller, so I think that’s enough of a testament to the potential of Playstation-style d-pads even for fighting games.
But in general, the DS4 d-pad is king. It’s soft, and yet firm; it’s completely non-fatiguing. It responds to a light touch, but with just the right amount of travel that it’s possible to comfortably tap a direction as fast as your thumb can move, unlike many other d-pads which are just too clicky or stiff to enable that (I’m looking at you, Xbox One d-pad).
In close second I’d say is the SNES d-pad, but it’s way too hard and flat and always bruises my thumb after a few hours.
And of course, you’re looking for one controller for everything. The DS4 has the nicest analog sticks around, and you’re not really going to find anything close with a third-party controller.
But above all else, with ds4win (which is a must; make sure you install Ryochan’s fork of the project), you can make the DS4 do damned near anything. No joke, you can actually use its gyroscopic sensors to control the mouse, which is actually my preferred way to play DS and 3DS games, since I find it much more precise than the little touchpad. And a nice bonus is the fact that you can change the Bluetooth polling rate manually, which hugely conserves battery life at the cost of only a fraction of a frame of input lag.
At some point you should invest in an arcade stick, though. That’s definitely the most fun way to play 2D retro games.