Microsoft are absolutely leaders in this area, and the gaming community as a whole should be grateful for their efforts. Who knows if the PS5 would've even focused on BC, if Microsoft didn't push it so hard during this generation. We all remember that infamous message from Jim Ryan, downplaying the importance of BC.
Though, from a sales perspective, I do think BC will be far more significant for PS5 than Xbox, regardless of if XSX BC's implementation is superior. This is mainly due to the respective user-bases for each current gen system. The PS4 has well over 100M people invested in the PS ecosystem, while Xbox is roughly half of that. If we suggest that the main short-term goal of BC is to retain current user bases, by extension, we might automatically see sales similar to the current PS4/XBO generation.
Regardless, MS is doing great work here, and I do hope their efforts bring them some success. I also hope that they can keep forcing the industry as a whole to be better re: BC - specifically for consoles.