Both. They need each other to live, really - PC's rely on consoles for a library of games, while consoles rely on PC's for their continued technological advancements. Without one or the other, the game industry would stagnate and crash.
Personally, I do believe that mice are more accurate and faster than sticks. I can whip around in a fraction of a second, accurately, with a mouse, while it will literally take even the most skilled player much longer to do the same. Mice are more accurate because they are an absolute pointing device, and you aren't fighting the constant motion of the sticks - There's a reason why many console games have aim assist, while PC games don't. If you take two gamers of fairly equal skill, one using sticks and one using the mouse, the mouser will have a distinct advantage because of this. Keep in mind that many Games For Windows Live games support using the X-Box 360 controller for control, but I can't say I know of anyone actually using the controller over the keyboard and mouse. It's a distinct disadvantage. However, that only really applies to first-person shooters; In third person games like GTA4, or in driving games, I much prefer a gamepad. In flight sims, I very much prefer a joystick. It greatly depends on the game which control scheme is more attractive.
@CaptainCool: As for games designed to work at optimal performance, I think you need to look at a few good examples of console games that don't run at a solid 60FPS. Left 4 Dead is an amazing example of a game that's been stripped down graphically, and yet still plays like total ass on the 360. Fable 2 has issues at times, as well, especially in areas with waterfalls - The frame rate slows to a crawl. Not that I think graphics options would help simply because the game is optimized as much as it is on a console, but the point is, on a PC, if this kind of thing happens, you more often than not can adjust settings or otherwise squeeze more performance out of it in various ways. You can also achieve a much, much higher quality in graphics for a similar frame rate than a console with even a budget gaming PC these days.
Also, PC's can output to a 5 billion inch TV screen, too - And with a decent video card, actually take advantage of its resolution, rather than scaling up to it from 720p like the PS3 (rare is the PS3 game that actually runs in 1080p) and 360 do.
The major advantage the consoles have over PC's is the accessibility and the consistency of the experience with services like PSN and X-Box Live. You don't have to deal with updating DirectX or your graphics drivers, you don't have to learn controls beyond the simplicity of the gamepad (which is actually quite complex compared to days of yore), and it's generally just easier to get into. There isn't really a major cost difference between a decent video card and a console, but there's still the illusion that gaming PC's are multi-thousand-dollar behemoths, which makes consoles seem more attractive. Consoles do crash, just as PC's do, and getting them up and running again can cost a lot more than a pizza and an evening with a techie friend, seeing as consoles aren't exactly user-repairable for the most part.
EDIT: @PATROL, you aren't seriously saying that piracy is a good thing, are you? Also, consoles require "upgrades", too - Each generation of console is phased out entirely after several years. Current PC's are entirely capable of outdoing any of the consoles available right now, and could continue to do so for a good while. The X-Box 360 and PS3 represent high-end PC's at around the time of their release, and to replicate their abilities, even just a modest rig (well under $1000 total, MAYBE $200 for a video card for a recent machine) will work just fine. Especially considering the case of Left 4 Dead, even the Low quality settings in most PC games are generally equal to that of the consoles, so realistically speaking, you could still be gaming on hardware released at the time of the 360's launch with about the same success. That said though, ports from consoles are generally quite lazily-optimized - Bad Company 2 is an amazing example of laziness, requiring a quad core CPU to even play smoothly.
