Hrm... it was definitely a mixture of things. But if I had to say one thing I suppose it would be the "exclusives" (I liked your 360 wording better ) for the system.
The Legend of Zelda: Twilight Princess was a big factor in buying the Wii on launch day, but I was also very interested in these "motion controls" that Nintendo was fussing about. So I bought titles like Rayman Raving Rabbids (fun!) Red Steel (let down!) and Dragon Ball Z: Budokai Tenkaichi 2 (loved using the controller to mimic the Kamehameha ). And of course, Wii Sports was there to keep the fun going. ^_^
For me, the order of importance was:
1. Exclusives/Overall library
2. Motion Control
3. Brand Loyalty
The others were just a bonus.