The quietest case of the two is the P182. I have the P180 and it is very quiet. Ours is loaded with 2 SATA drives, a DVD burner and CDROM, Nforce4 mobo with 4x512 memory and things stay nice and cool. The CPU rarely ever gets much over 45°C while gaming. But then, we do have a Zalman CPNS7700 on it. A nice touch are the dust filters at the front of the case.
The Antec 900 is undoubtedly the coolest of the two, but also generates a bit more noise. It also offers more room to work in. Be prepared to be doing some regular cleaning of the dust bunnies as there are no dust filters and plenty of openings for dirt and dust to enter.