Can xbox1/ps4 can download an play old games?

like my ps vita lets me download an play ff7 and fftactics from the ps1

xbox 360 let me download old games like halo 1 etc

now if i buy a ps4 and i purchased ff7 on my psnetwork account can i play ff7 on ps4 through my ID or no?

also can if i bought old games on my 360 can i play them on xbox one yes or no?

No. Although, some psn games have been upgraded for the ps4 and can be re downloaded for free if you already bought it once they are available. But the selection is small right now and as for ps1 games, Sony is supposed to give details soon on its cloud gaming service in 2014. It supposedly, will allow ps+ members to stream and play all of playstation's previous consoles games off the ps4. So far Sony has been real quiet about it...

I hope sony knows that I don't want to do cloud gaming

I want to OWN the game on my hard drive not someone elses

and i want to play it from MY console not someone elses

cloud gaming is the worst idea ive ever heard of

i like disc or downloadable games ONLY no cloud service EVER

i am going to get a ps3 until sony fixes the ps4 an lets ppl play games on it

The hardware in the ps4 isn't compatible (no PowerPC?) so they would have to "re do" every game you want to buy and upload it to the ps4's psn which would take forever to get the library that the ps3 has gained over the years. Plus research shows, people don't buy new consoles to play older games on them, people that do is a minority. Cloud seems like the only to get a ton of old games on there fast, if it works. Nowadays you technically don't "own" anything anymore so you might as well live with it.