I'd have to second ERP there. It's not just the ease of the platform use, it's also the fact that XBox offers by far the best compiler solution at the time.
Basically, which ever platform has Visual Studio is the easiest.
In that case they'd all rate the same
SNSystems ProDG offers MSDev integration for some time now. I think Metrowerks offers something similar as well, though I haven't used it, so I am not sure how well it works.
Actually to be fair we've used MSDev throughout development of our game, linked to external stuff. After switching to SNSystems tools, the integration was just more complete (no more external makefiles, native win32 compiler instead of calling networked linux one, debugger IDE etc).
What process do you go through to program for these machines? What OS/Compiler is used
As I mentioned above, at this point both platforms offer development tools that allow you to basically stay under Win32&MSDev all the way. So all you need is the software, a devkit, and a win32 workstation with a network card.
Compilers I know for PS2 are GCC (Linux/Win32(ProDG)), CodeWarior, and VectorC. I don't know much about the last, except that it looks interesting for offering C++ -> VU compiler.
GCC also has CW and ProDG, not sure if there are others, maybe ERP knows more there.