I have been searching Google all day and cannot find any real information. I'm looking for information in detail, such as specifications or the qualities of the GPUs that make the differences.
Summary: different approach to calculations. Nvidia GPUs are more like CPUs, in that they have only a few processors that do work, but faster. ATI GPUs have slower processors, but a lot more of them.
You can find a more complete description on the relevant wiki page :
Firstly, AMD designs GPUs with many simple ALUs/shaders (VLIW design) that run at a relatively low frequency clock (typically 1120-3200 ALUs at 625-900 MHz), whereas Nvidia's microarchitecture consists of fewer more complex ALUs and tries to compensate with a higher shader clock (typically 448-1024 ALUs at 1150-1544 MHz). Because of this VLIW vs. non-VLIW difference, Nvidia uses up more square millimeters of die space per ALU, hence can pack fewer of them per chip, and they hit the frequency wall sooner than AMD which prevents them from increasing the clock high enough to match or surpass AMD's performance. This translates to a raw ALU performance advantage for AMD:
AMD Radeon HD 6990: 3072 ALUs x 830 MHz = 2550 billion 32-bit instruction per second Nvidia GTX 590: 1024 ALUs x 1214 MHz = 1243 billion 32-bit instruction per second
This approximate 2x-3x performance difference exists across the entire range of AMD and Nvidia GPUs. It is very visible in all ALU-bound GPGPU workloads such as Bitcoin, password bruteforcers, etc.
Secondly, another difference favoring Bitcoin mining on AMD GPUs instead of Nvidia's is that the mining algorithm is based on SHA-256, which makes heavy use of the 32-bit integer right rotate operation. This operation can be implemented as a single hardware instruction on AMD GPUs (BIT_ALIGN_INT), but requires three separate hardware instructions to be emulated on Nvidia GPUs (2 shifts + 1 add). This alone gives AMD another 1.7x performance advantage (~1900 instructions instead of ~3250 to execute the SHA-256 compression function).
Combined together, these 2 factors make AMD GPUs overall 3x-5x faster when mining Bitcoins.