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Xbox 360 won that gen.
Actual sales numbers were neck and neck, but the 360 was definitely more popular in the USA and that's where a lot of the worlds media comes from so it had an outsized cultural impact. I think that generation did define what still seems true today that Microsoft are the masters of software and Sony the hardware.
Sumo-
To be clear, i was talking about console design...
But I disagree re: hardware too. PS1, PS2, sure; iconic designs. Xbox 360 was less powerful on paper but Sony made the PS3 impossible to code. It's a large reason why they're still ignoring backwards compatibility.
PS4 vs Xbox launch hardware was an easy win for PS4 but since that, all revisions have been better handled by Microsoft both aesthetically and in terms of hardware engineering. The PS4 Pro is massively limited by its thermal envelope because whoever designed it had no idea what the were doing. The One X, however, has a fantastic thermal cooling design that allows for more power than the PS4 Pro and in a smaller footprint.
It looks to be the same for the Series X - more powerful console (we'll see by how much but on paper at least...) in a much smaller footprint.
Soul
PS2 was iconic and, as @Sumo said, the logo you could turn was a class touch. OG Xbox was a joke in comparison.
PS3 was shit - Xbox 360 won that gen.
OG Xbox One was horrible but the One X and One S were better than the PS4.
I definitely agree that a console should be minimalist and unobtrusive in design. Just don't understand where PS5 is aiming at? Maybe the West Coast Customs / pimp my ride sort of customer?