If this conversation would take place in the PS1 era, (i.e before Super Mario Galaxy) there'd be a slight chance I'd consider Sony. (Nintendo still has the most platformers, but if we're only looking at the singular best platforming game of all time.)
I'm a big fan of Crash Bandicoot and Spyro, but Nintendo would still take the cake. And since then, the gap has only stretched in Nintendo's advantage. Sorry Sony. You've got some excellent platformers, but in this particular genre, Nintendo is unchallenged.







