The Xbox One has these modes, from the top of my head (and a little bit simplified). The following pertains to CPU/GPU only, not memory as I think these are fixed (say, 5GB for Game, 3GB for OS, though we don't have any confirmation of these numbers on either platform I believe)
- game only (90% of resources for game)
- game with OS app snapped (40% of resources for game), so showing both game and OS/App at the same time in 3:1 vertical split screen mode, similar to how Windows 8.0 supports it (but 8.1 goes further, allowing 5 Apps snapped side by side, and no fixed division)
- game with OS on foreground (10% of resources for game, so game can still send notifications and such, keep network connection, etc.)
I don't think the PS4 has the 'middle' mode, and whatever you don't have at launch, it will be hard to catch up on.
That's the general thing here - there are some tough choices made at the start of the new cycle. It's easier to drop something if it doesn't work than add something that you were missing, especially if all games need to support it / be tested against it.