Why would the PS5 have the higher install base? They can still fuck up like they did with the PS3. Just like how MS fucked up current gen.
Sony still needs to sell the machine, and they haven't even started yet. Way too presumptuous
The ps3 launched at the current equivalent of $750. Sony knew it would be losing marketshare but considered it "worth it" to push Blu Ray and Cell in the market.
It outsold the 360 every year the two were on the market despite the massive gulf in price points and lower third party support.
The two systems were "tied" only because MS launched a year earlier, AND the 360 got a 20millionish mid generation bump from the Kinect, which isn't a thing they could repeat with the XBO.
The fact is that Microsoft simply does not compete in 2/3rds of the world where Sony sells systems. There's no way around that. Since we know Sony isn't launching an insanely expensive box a year late this time there is no way for Microsoft to "win" the generation by running up the score in the US and UK. This is especially true given that vendor lock in to both ecosystems is high. No one wants to "lose" their digital catalogue or friends lists.
The generation is already decided, which is why MS's focus is on generating revenue through other means than selling console boxes.