Some games really feel like they're built for controllers and playing them any other way is a pain. Especially in an era of smart-buttons, long-press actions, and hold-menus in console versions, if those options are all just bound to keys and the menus are taken out then I can find the keyboard a real pain (even with a few mouse buttons to balance the load). I definitely think the controller mods that re-enable the full controller support for the Mass Effect PC titles are essential.
Shooters using a controller take a very different skill than mouse but I've been doing the former since Halo 1 and the latter since Quake 1 but at this point I find both are fine as long as they're implemented correctly (it's easier to implement it badly with a controller [you do need to play with curves and the deadzones to get a good feel - I have certainly done tiny tweaks to controller code in projects that have hugely improved the feel so I totally get how something like competent Uncharted 2 controls can be broken by minor tweaks into Uncharted 3 and require them to get fans into the studio to explain how to tweak it back to being good] vs just not using mouse acceleration and leaving a sensitivity slider for me to define).
So, having said it's very much a game-by-game question, there is also the big divide: mouse and keyboard means I walk or run and can toggle a different speed (sprint or walk modifiers) but a stick means I've got analogue movement control for not only speed but also direction. That's huge and in some games I really want to focus on how fast I'm moving, how much noise I'll make, and exactly what direction I'm going relative to where I'm looking. In other games, I really want to be able to be precise and quick about where I'm looking and even the best controller configuration (and a generous auto-aim) can't beat a decent mouse. That compromise means I'll be on a mouse in any competitive shooter mode (and if I play that mode with the mouse then I'll play the solo campaign or co-op the same way) because it almost always works out that that is the key factor to competitive shooting.
They're both great (a 360 pad or DS4 are both not that expensive, neither is a decent gaming mouse like a mid-range Logitech and they're all so well built to feel good) and a lot of games are totally playable with either. I really wish some more effort went into porting controller design (with limited keys) onto keyboards so we could choose between various efficiency options (short tap vs long press combo of two actions on a single key) and just splitting everything onto a separate key.