From what i have seen, very few Xbox 360 games install data on the consoles. A lot of the newer ones do sure, but in the past no, because the original Xbox 360 came with only around 256MB of hard drive space. But with the PS3, most games install large chunks of the game onto the console. MGS4 was so huge for example, that the game had to reinstall a different part of the game for each ingame chapter, to save hardrive space.
Now anyone who has ever played battlefield 2 (or even Halo 3) will know that loading times solely from a disc SUCK. You have to wait ages for the pre-rendered textures to load from the DVD. Now, if we install 75% of those textures onto the actual console, the console can read them faster. I don't know exact numbers, but loading from the hard disk is at least 10x faster than loading from the disc. And considering the figures just mentioned showing how Blu-ray is read faster, it means the PS3 can load more pre-rendered textures from both the disc and the hard drive, at a faster rate, therefore freeing up more VRAM.
But the Xbox 360 can do that too. It can read the HDD slightly faster aswell, or so i have heard. So they are about the same on this level.
But the GPU of the PS3 is faster (ever overclocked your graphics card? Its the same effect, think of the PS3 as an overclocked Xbox 360), which means you don't get that 'lag' effect when the textures on screen change, regardless of how many of the textures are pre-rendered or not. This is probably the single biggest limitation of the Xbox 360.
In my opinion, the key to better graphics is simply having a larger HDD to install the pre-rendered textures, but i'm sure theres more to it than that. So far, i think developers for the PS3 have taken advantage of this more than some of the Xbox 360 exclusive developers.
Despite reading so many theories, i still have no idea how cross-platform games are different on each console. This leads me to the conclusion that that have not ported them correctly, because there are some cross-platform games which are exactly the same on both consoles.
On another note, PCs are faster and more often than not, have more and faster VRAM, Faster and Larger processors, Faster and larger harddrives than the playstation 3. So they are better in every way. Except for cost.