Okay here's the comparison. The world's leading authority on computer science here (self-proclaimed).
The Xbox 360 can potentially do free z-buffer and frame-buffer operations - but due to exceptionally low main memory bandwidth - that doesn't help too much. That's what we really need. It's limited by the main memory bandwidth. The main bottleneck:
25,600,000,000 bytes per second / 60 frames per second = 426 Megabytes/frame
How many vertices can that support? 32 bytes per vertex, gives:
426,000,000 bytes / 32 bytes = 13.3 million vertices per frame
However - the rasterization requirements vary tremendously. Let's assume 5 z-compares per vertex, 5 pixels, that'll raise the bandwidth requirements to:
13.3 million vertices per frame * 60 = 798 million vertices/second
798 million vertices/second * 5 * 8 bytes (z-read, z-write) = 31.920 GB/s of z-buffer bandwidth
It has the on-board z-buffer. However, in actuality, it needs half that memory bandwidth for textures. Thus it only needs half of that for z-buffer bandwidth. 16 GB/s of z-buffer bandwidth. How much memory bandwidth does it need for the textures? Let's say the scene is at 1280 x 720, with 2x AA, 32-bit textures, 4:1 texture compression (actually 8 bit textures), and trillinear filtering:
1280 * 720 * 1 byte * 60 frames per second * 8 samples (trillinear) = 442 MB/s
But let's say we wanted to do more advanced forms of texturing:
1920 x 1080 * 4 bytes (no compression) * 60 frames per second * 16 samples (anistropic filtering) * 4 samples (4x anti-aliasing) = 31.8 GB/s
It only has 25.6 GB/s. Thus - it has a disadvantage in the texturing and resolution department to Playstation 3, although it has an advantage in raw vertex pushing. Because Playstation 3 has a CPU which can do vertex pushing, and it can dedicate its GPU just for rasterization (with all 25.6 GB/s available for that), while Xbox 360 can't, Just about equal therefore. It could really use an on-board texture cache as well - then it would not have that disadvantage in texturing/resolution. Gamecube uses a texture cache.
So their GPUs are just about equal, in fact, they have similar transistor counts, but in the CPU department, with 25.6 GB/s of dedicated memory bandwidth, and 7, 128-bit SIMD mulitply-adders, the Playstation 3 is light-years ahead.
Thus the winner in terms of overall performance is of course Playstation 3. Although it takes a little effort to use it all.