The issue with the consoles wasn't the choice of manufacturer or the specific type of CPU or GPU, it was that both of the main console vendors chose to go for a sales price of near $400, and a mostly unsubsidized hardware.
At that price point, the total budget you have for the major silicon, that is, GPU, CPU and RAM, is well below $200. Both of the modern consoles at launch spent less than half on the main parts than the previous gen consoles did. At this price point, I really cannot see any discrete parts winning over an apu solution. Remember that discrete parts cause significant additional expenses in high-speed signaling and the like.
So, as the price point necessitated an APU, the choice of manufacturer was really simple. IBM had no decent GPU, nVidia had no decent CPU, Intel would have been way, way too expensive.
The choice between the small and big cores is interesting. The best big core that would have made the mfg cutoff was probably Piledriver -- apparently both of the vendors decided that the weaker cores were better.