As I know, it went something like this:
-Both wanted x86 for better usability (PS3 Cell was a hard-to-tame beast for many devs, ARM not strong enough)
-Intel was not interested in manufacturing semi-custom chips
-Nvidia simply did not have x86 licenses
-AMD was left as the only option
Of course other things also factored in the big picture, profit margins for example, but those are more known.