We tested six multiplatform games on both consoles and every time, the PS4 was under a minute while the Xbox One install was several minutes long and required downloading an update before beginning the installation. When you include downloading those updates for each Xbox One game that happen in the background on PS4, the install times can get as high as fifteen minutes before you can even launch the game.
Assassin's Creed IV:
Xbox One (offline, no update): 5 minutes 50 seconds
Xbox One (with update, fastest connection): 7 minutes 2 seconds
Xbox One (with update, 10Mbps connection): 10 minutes 32 seconds
PS4: 42 seconds

The rest of these were tested on our office Wi-Fi which is around 9-11Mbps. It may have been faster on a wired connection, but you can compare your own connection speed here. These are our results:

Need For Speed Rivals:
XBO: 09:25 (including update)
PS4: 00:32

Just Dance 2014:
XBO: 08:48 (including update)
PS4: 00:45

NBA Live 14:
XBO: 16:26 (including update)
PS4: 00:35

FIFA 14:
XBO: 16:06 (including update)
PS4: 00:34

Madden 25:
XBO: 9:38 (including update)
PS4: 00:38

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