Centrino is a mobile platform by Intel consisting of a CPU, wireless, and chipset.
Centrino itself is not a processor.
Right now I think Centrino platforms use the Penryn Core 2 Duo processors only. The future ones are supposed to support Nehalem architechture so I don't think Core 2 Quad will ever be under the Centrino name.
Mobile platforms enhance portable computing by doing things like extending battery life, etc. Phenom II is a desktop processor, you can't really compare it. As for Centrino vs. Core 2 Quad, i'd say for most purposes, Centrino is more than enough.
Didn't see you said gaming PC. For gaming pc, core 2 duo will be fine unless you play a bunch of quad-optimized games. In that case maybe you're better off with the C2Q.