Both PS4 and Xbox One install the entire disc onto the hard drive. Both can do this in the background while you play something else, unlike last gen where both made you wait on the install screen. 360 however was optional install though. I didn't buy system based on controller. I bought them based on the type of games they have. Last gen, the 360 clearly had better software and online network, especially the first half of the decade of its life. Then the PS3 software line up closed in. This gen, both are essentially the same. However, if you like Japanese niche games, the only home console to play them is the PS4, and occasionally PC. Microsoft pulled out completely from Japan this time and in return, Japan ditched them. I have always purchased Microsoft consoles first in the past because of their software line up and their willingness to pull Japanese developers in. Not this time. I bought the PS4 nearly two years ago and just recently bought the XBO only because it was cheap during the holidays to play just a handful of exclusive games on it, and maybe a small few that perform better than the PS4. Yes, I value Japanese games more than western games. You know, the ones with cool looking dudes holding swords or chicks with skimpy outfits on the game covers vs muscular hairy males holding guns. xD
For the controllers, IMO the 360 pad was the best and it's a hair better than the XBO and PS4 controllers in terms of overall ergonomics. Besides the D-Pad, it's essentially perfect, a very durable controller with no bells and whistles and natively works on PC. As for the OG Xbox controller, I didn't like the super sized launch pads. The later revised Controller S was great, but the 360 pad also destroyed it. One feature I did like on the OG Xbox and PS2 controllers was the pressure sensitive buttons. That was removed and never came back in later gens.
The Wii U, I have that too and it has its exclusive games. I have about 10 games on it and they are all very good, but it's nearing its end and I only see a couple more games that I might buy for it. The funny part is, I probably will end up with more Wii U games than Xbox One games in the end of both systems' life.