I've only scratched the surface of the PC version since I'm still not done with the game on PS4, but based on my short time with it (40+ hours), this is how I find it compares with PS4 version:
- PC version loads almost twice as fast in my case (SSD vs regular PS4). 6.6 seconds to load the first stage on easy vs 11.2 with same character and settings on PS4. Stage 80 was roughly 3.3 seconds on PC vs. 6 seconds on PS4. Other stages gave similar results.
- Texture loading happens very fast on PC. On PS4, like many Unreal Engine 3 games, it can take a few seconds before the textures are fully loaded (and again I'm using SSD compared with a regular PS4 hard drive).
- PS4 has a very short break, a slight stutter, when spawning new waves, which is almost absent from the PC version.
- Some menu text in the PS4 version is upscaled, where as it renders natively on PC (only tested it at 1080p).
- PS4 version runs entirely without anti aliasing. On PC you can do the same and there's an option to turn it on, though it doesn't say what kind it uses (FXAA?).
- PC version supports dual language options, while PS4 doesn't.
- PC version doesn't have full controller support. In order to start the game you have to name your save file with a keyboard, something most people won't have a problem with, but speaking as a big picture comfy couch gamer it is annoying, even if it is a one time thing.
- Online is easier on the console version due to a standardized interface. On PC even finding or sending an invite can be difficult until you learn you need to press right d-pad when standing on the proper option menu. I also had difficulty with the voice where I couldn't get Steam chat working, because the game somehow interfered with it, but on the upside the PC version doesn't require a subscription to play.
- There seem to be more hackers on PC, which can ruin your progession if you play with random people. It's not a big deal to me since I mostly play with a team of my friends, but if I didn't I think I would go with the console version because of this.
- They removed region locking from multiplayer on the PC version, but it's still in place on PS4.
- Performance is night and day in this. At times my PC (i7-6700k/GTX 980 Ti) outperformed the PS4 version by a factor of ten or sometimes even more (2-3fps becoming 20-30fps) and in general play it's much better. It isn't perfect and with how much is going on it never was going to be, but after playing the PC version in the weekend it took some adjusting returning to the PS4 version at my weekly EDF meet-up.
While I prefer it on PC, both versions come highly recommended if you enjoy coop shooters. It doesn't get any better than this.