Only a Wii U owner here, but I'll say what I know...
Every game I've heard of needs to be installed. With sizes of today's games, the optical drives just can't pull the data off of the discs fast enough to hide load times (or make them somewhat pleasant). I believe every game fully installs, so the disc, should you use one, is just there to verify you haven't sold, traded, or loaned the game you are currently playing.
I think the PS4 has the nifty feature to install a game and allow you to start playing after a certain part is loaded to the HDD. It doesn't matter if you do it with a physical disc or download it from PSN.
If you are looking to buy an xbone or PS4, it might be a good idea to get one with the larger hard drive. The 500 GB drives can only hold maybe 10 games (counting the OS taking up 100-200GB). Don't forget the patches that are now routinely over a GB in size. If you don't replay many games or don't mind the occasional reinstall, 500 GB might be fine.