Sony still not pursuing backwards compatible for PS4.

[Roberto10]

You can't emulate PS3 games in PS4. But neither can X1 emulate X360 games.
Microsoft on e3 said that you insert the physical disk, it performs an authenticity check and then you download the full x360 game in your machine (which they have already ported to X360). The disk acts like a "voucher" that allows you to download a game to X1 for free. Now if it works the way I think it does, this has two problems: The first one is download and install time. So depending on your connection speed you might need hours before you actually can play the game. The second problem I see is HD space. If you have a large library and want to store all your X360 games in your X1 then you need lots of space.
Now the way sony could implement this is by allowing free unlimited use of PS Now for a specific title if you owned the PS3 copy of the game. The only drawback would be that you need to have a good connection to play your PS3 game but I think we all would agree that it would be better than nothing. That would even help them promote PS Now as a service (If I constantly keep playing my PS3 games through PS Now I might try out a new title, whereas now I dont even know how to set it up).
The only reason this is not happening is because they are market leaders and they don't have to (plus they want to keep making money off PS Now). If they see X1 gains huge popularity due to BC, I'm sure that they will implement a sort of BC of their own.
One final thought. I remember when my PS3 used to be BC with PS2. That was huge because when I bought the console I already had a huge library of PS2 games (and was one of the reasons I chose PS3 over X360). That being said I didn't even use the feature once. I had my ps2 for ps2 games and my ps3 for ps3 games. So BC in general isn't that big a deal for me.