I won't buy either out of the gate, just too damn expensive. But once price drops happen, then I'll be considering a next-gen purchase. Besides saving money, the other advantage to that is that you can see what's gonna happen. You'll be able to see what games are coming out for each, how each performs, and how much 3rd-party support it gets.
If I were to choose right now, based on the information we have; PS5 all the way. Xbox's game reveal event was lackluster to say the least. Here's to hoping the next scheduled event (sometime this month, IIRC) is more of a wower. Because I have been more of an Xbox man, myself (though I do own a PS4, as well).
But man, if the PS5 rumors about full backwards compatibility turn out to be true, that's big swayer for me, too. I have an extensive PS1 and PS2 library that I wouldn't mind seeing in HD.
I know it's a cloud-based service. But that doesn't necessarily mean discs won't work. I mean that's how the XBox One backwards compatibility works. You stick in a disc and it just authenticates that you own it then downloads the game from a server. I really hope that's the case with PS5's, as well.
