I'd say it's pretty obvious what my console preferences are at a glance of my collection or at my signature.
As for why I preferred the 360, there were a few reasons.
First was the controller. It was a solid, comfortable controller that didn't cause hand cramps after using it for a while, unlike with the Dualshock and Wiimote. I honestly thought it was the pinnacle of controller design until the One came out and managed to make a great controller even better.
Next were the achievements. Having those goals for each game to obtain was something that really invigorated me to try to play each game to it's fullest. And they also had the bonuses of being a chronology of my gaming time as well as being ultimate proof of what I accomplished. Granted, the PS3 did come out with trophies after a while, but they've never really clicked with me as well as gamerscore did.
And then there was the online component. While Xbox Live did have a cost unlike PSN or WiiConnect, it really felt like a case of getting what you paid for. Matchmaking and other online modes were smoother and more reliable. Additionally, cheating was also not as prevalent as it was on the other systems, but whether that was because of the cost of the system, Microsoft's moderation team, or a little of both, I'm not fully sure. There were also good bonuses for having the service, like the Gold-exclusive sales and now Games for Gold, which will usually more than compensate for the small fee of the service.
As for the Wii, there were quite a few solid games that made it a good secondary companion to a 360/PS3. I'd say it's biggest problem wasn't the motion controls, but how there was no middle ground for them. The motion controls would either feel fantastic and natural or unresponsively frustrating; there wasn't really a middle ground. And when coupled with the idea that if a game is on Wii, it must have motion controls, most games fell to the lower end of that spectrum. It was pretty obvious which games had the motion controls tacked on and which ones took the time to properly integrate it into the game.