I think it varies rather greatly. For instance, when I was younger I played the hell out of shooters online on my PC (Rainbow Six/Rogue Spear/Counterstrike/Battlefield 1942 + Vietnam) because they were just much better than the options on the consoles at the time. Heck, there hardly were any decent options on consoles.
These days though, and I think this is a big influential factor for a lot of people, those shooters are not only on consoles, but the majority of my friends have consoles rather than a decked out PC. In order to play with them I play on the PS4 (Xbox360 last gen), and so I generally play FPS games and the like there. While a mouse and keyboard is the way to go for shooters, the PS4/Xbox controllers are actually great for FPS games as well.
Otherwise, on my PC I play all of those other genres that the PC offers a superior experience on, specifically 4x games, city/colony builders, RTS games, mmo's, grand strategy games, and open world RPG games (the modding community really makes those major open world games faaaar better on a PC).
I suspect other PC gamers have similar reasons... FPS games are more fun with friends, and for a lot of us (if not most of us) the majority of our friends will be on consoles which don't offer a cross-platform experience. Given the difference between the mouse + keyboard and a controller (the former having a big advantage), I doubt we'll ever see cross-platform play as well, so I imagine FPS games will be more common on consoles than most genres.







