Assuming I had a 360 it would likely still be PC unless the port was really, really awful by the time I got around to caring (normally around the time the second major patch appears after the first glut of them).
I have TV out (and some half decent projection equipment if I am lucky) so big screen is not a problem (my PC monitors are more than fine for games and video anyhow). See my recent disparaging of "HD" if you want for more on that.
http://gbatemp.net/index.php?showtopic=73993
I have a couch/bed available for PC gaming and some rather curious stuff involving extensions (me+ soldering iron/connectors + lengths of wire: not a good idea if you are afraid of wiremess) but my PC chair if I need it is quite comfortable for what it is worth (I figured I would include it under the same reason for getting a good mouse, keyboard and monitors).
Online I do not have to pay for (I have usenet instead if I am going to pay for something) even if I am supposed to pay as there are free options if you know where to go (the "complexity" of getting there often means I get some decent opponents rather than most xbox live users I have the misfortune of meeting). "Achievements" I have not cared about since the days of arcade games and being immature with the high score boards.
Complexity: somewhat of a myth as far as I am concerned for actually getting stuff running. Patching (if necessary) is normally easier than finding a crack (I crack all my stuff regardless purely as it makes life easier) or following a guide (although the same 5 steps tend to apply).
Controls: I tend not to play sports/fighting games but for just about everything else keyboard + mouse trumps any controller (which I also have should I somehow need one).
Mods: there are some for the 360/consoles but PC is where it is at.