For the Xbox 360, they ditched Intel and went for PowerPC. Microsoft then bought a bunch of PPC Mac Pros from Apple for development since they shared the same ISA :D
That entire generation of consoles, the Xbox 360, PS3 and Wii (and then arguably the Wii U) were all some form of PowerPC.
The following generation though everything switched to more commodity hardware, with the PS4 and Xbox One using x86_64 processors and the Switch using an almost off-the-shelf SoC from nvidia.