The highest level of PC gaming I played was CAL-M for CoD2 PC. I've played on many different competitive teams for the PC and a few for the console as it started to gain momentum. The fact is that there will be more console copies sold than PC copies and most likely that will translate into more competition. I'll have to do some research later but I would would guess that this will mean more competitive teams in leagues. I'll do some research on CoD4 later but today is my only day off from work so it will have to wait.
I totally agree that public play is not where competitive are played. Even if I wanted to play a scrimmage, I would always join a PUG match and never just join some public server. What makes FPS fun and competitive for me is playing as a team. CoD4 allowed hosting private matches and I would assume that CoD6 will as well. This is where all league games will be played. I don't know what settings they will allowed to be changed but they have always been good in allowing these options for console, since is a large community of players who play leagues. I've got some friends at Activision who will start work on CoD6 next week and I'll have a better idea of what is possible.
It's simple...if you prefer using keyboard/mouse that much than play PC. But if you would like to play with larger player base, less cheating, and on the main SKU then play console. As for which is the more competitive platform....we will have to wait and see, but I'd be willing to place a cash bet that there will be more teams competing in console leagues than PC leagues.