I wouldn't pick a Nintendo system even though you excluded us from picking it. And why is the Neo Geo excluded? In my opinion it's a very singular focused console.
That being said as much as I want to say the PS2, many of my favorite games are ports, so not including that I would actually have to say the 360 has the strongest library of all time. It just has an obscene amount of variety not to mention some of the greatest 3D games ever made.
If the OP meant largest when they said strongest, as in, the most amount of heavy hitters in each genre available on one console I would definitely say PS2, even though its not my 'favorite console...