I have both so I will try and answer this from an objective standpoint.
Quote: "I've heard that the PS3 is quieter than 360"
Very true. During play, you won't notice the 360 too much, especially not the Elite version, which has a quieter disc drive.
Quote: "I also heard the ps3 doesn't have render problems as much as the 360 has"
Completely untrue. "Render problems" is an issue of the game title -- not the console. If anything, the graphics processor in the PS3 has less power than that of the 360, which also hampers the graphics on the PS3 somewhat, given the way most modern games are built.
On the other hand, the PS3 has a lot more raw processing power, but generally of a kind that is not optimal for games. There's a reason why Kutaragi is no longer the chief engineer at Sony's entertainment hardware division.
Quote: "free online play"
Yep. But Xbox Live has a far better service, if you ask me. Most probably because it's been around for several years more than PSN.
Most features of PSN is essentially the same, except not as good, as on Xbox Live. Besides, having to first download and THEN install things has had me simply looking at trailers on the Internet and trying demos on the 360 instead. It's simply too tiresome.