PS3 had BC last gen until Sony saw that the extra cost didn't brought extra revenue and cut it out. So that pretty much show that listing BC games to pad list war is laughable. You may love some or even all of the previous gen games, but a very very very small number of people would buy new consoles for the intent of playing old games they already had console to play it on.
Not to take any sides, but the PS3 never really fully got rid of back compat. Every PS3 (even the slims) can play all PS1 disks. And to make up for PS2 BC removed they released several game collections like ratchet and god of war.
Even during late last gen Playstation/Sony still valued their old games greatly.
Bet with Intrinsic:
The Switch will outsell 3DS (based on VGchartz numbers), according to me, while Intrinsic thinks the opposite will hold true. One month avatar control for the loser's avatar.