Neither are backwards compatable, but sony does have its cloud gaming platform which will enable you to re-buy ps3 titles and run them emulated some point in the future and MS are saying they will eventually do the same for xbox classics.
Xbox One has been such a mess of corporate rubbish and turnarounds its difficult to trust anything they say at the moment.
Ive been an xbox user since the first sku and this time round im going PS4, reasons for this are one the power adaptor is in the console so no brick behind the tele, the ps4 will run PS Plus out the box if you have a subscription (which i do) PS Vita Crossplay is massive, i can be playing fifa and at a push of a button stream it to my Vita while the OH watches some rubbish. MS is all about the tv service and it hides Lovefilm, Netflix etc behind the wall that is xbox gold, while Sony have this in the front menu regardless of which level you may subscribe to.
TBH its a tough call this time round, but PS4 just edges it for me.