Design question for GPU
There are a number of architectures, actually. And they're not as different as claimed by the different vendors (although there are still differences.)

NVIDIA typically builds GPUs that work a lot like general-purpose CPUs: There's a large framebuffer out in GDRAM, there's a number of large caches for texture fetch and buffering, and there are groups of pixel processors (typically 4x2 pixels) that operate on some particular primitive at a time. For framebuffer blending or writing, the I/O goes through the memory bus, somewhat helped by the caches. If multiple different objects cover the same pixels (overdraw) then the same pixels may go to/from the framebuffer more than once during a particular frame.

POWERVR and Intel typically build "tiled" processors, where they have a similar architecture (4x4 tiles IIRC) but to avoid the big input/output load on the GDDR, they sort all the primitives ahead of rasterization, so they only need to load/write a particular block of framebuffer pixels once per frame. At least, that's their design goal -- this is not always necessarily achieved. The benefit is that you need to spend less bandwidth on reading and writing back framebuffer pixels. However, approximately the same amount of texture bandwidth is used, so the savings aren't necessarily orders of magnitude (it's scene dependent.)

The Xbox architecture is a bit of a hybrid -- it has EDRAM that's bigger than itty-bitty tiles, but smaller than a full HD framebuffer. The GPU runs through the primitives, and writes them to the EDRAM, which then "resolves" to the output framebuffer (this also calculates things like anti-aliasing.) The EDRAM framebuffer is made to be effectively fast enough to be non-blocking. The screen will be split into some number of tile areas -- 1 through 4 for a particular frame, typically.