There's nothing to install when you download the game. You download the whole game directly to your hard drive, which is essentially what installs from the disc version. I know I have BF3, 2K and Killzone on disc, and the install sizes for them are all huge (36gb, 46gb, 39gb). So unless they changed it up, then the disc install and digital download are the same.
The problem is the games are pretty big in size. With a 500gb HD, that means space will disappear quick as hell. What sucks, is that even if you have the disc version, it still has to install it to your HD, so the only way you can really save space is to delete the data when you're not playing it, but then you have to install it every time you wanna play, which takes time. If you're gonna play the game, and beat it, then delete the data, you're still using the same amount of space as you would digitally. The only advantage is that you can delete it and either A. sell the game, or B. have it for quick(er) install later if you're gonna go back. With digital, you'd have to download it again, which would be a pain, and obviously you can't sell it.
Personally, I prefer digital. I don't tend to sell my games, and my internet connection is fast enough that my download speeds are pretty quick. Again, the problem comes down to space. I upgraded my PS3 HD, and will no doubt have to do it with the PS4 also. Just gotta find one that's big enough, as I only wanna do it once.
@We Ready
but i'd still rather get the disc.
memory cards