The new generation leads to bigger games, and hopefully more and bigger better content.
This will take more storage-space. But once on HDD, you have much better load-speeds.
Installation is not that big of an issue - on disk-versions, I think.
A modern bluray-drive wich is in next-gen consoles are much faster than what were in PS3, and atleast on PS4 it streams from disks to harddrive while you play - and I think someone in Microsoft said somewhere that they were also doing that.
So you'll not have half hour installs this generation from disks.
Mark Cerny confirmed that it would wary abit depending on the titles, but on his game, Knack - 34 GB free space where required for Knack - you'd be playing after around 10 seconds after you launch the game the first time - and while you play it keeps installing in background. It will wary from title to title. - So even if you do need to delete the gamedata for a game, it's not that much work to get it back again on diskversions.
On digital versions it's different, it's the same 'Play-Go' system there, but needless to say your internet is alot slower than disk-loading from your console.
So there developers will get creative - if they want you playing as quick as possible - one title we know is creative, is Killzone when you start downloading Killzone, PSN-store will ask if you want to play multiplayer first or the campaign.
If you select campaign, it will start downloading singleplayer data first, and after a few gigabyte, you can start playing while the remaining singleplayer-data at later levels downloads, and multiplayer data download after that, while it's the opposite if you select to download multiplayer first. :-/
So seemingly the console-manufacturers have put alot of tought into this.