The graphics on both the Xbox 360 and PS3 are the same. Most of the multiplatform games on the PS3 don't use the it's hardware to the point where it looks better than the 360, and even the exclusives don't look that much different. There's only some sharpness difference that's barely even noticable.
The "internet" depends on your router and modem and all that. If you're talking about the online community, the PS3 seems to be dead, or either full of annoying kids (free online = more kids).
Both consoles don't really crash if you play it for normal periods of time. If you play the PS3 for over 7 hours, it will crash, same with the 360.
The games are basically the same for both consoles, because of multiplatform titles. If you want more stealthy sneaky games and racing games, go for the PS3. If you want more shooty-fighty, slissy slicy games, go for the 360.