I have a spare 500GB WD harddrive hooked up to my Wii U, and use it for all of my save files plus Mario U and Nintendo Land (so far). I have not tried to install my disk games on the HDD, because I don't remember reading anywhere that it was possible to do so. At the very least, there is no obvious message that pops up asking if you would like to install a disk game.
This particular HDD powers on and off with the Wii U. (It has an external power supply, and I leave the HDD power switch set to ON.) It also appears to go into a "sleep mode" if it hasn't been accessed for awhile. Then, when I do start up Mario U (for example), it takes a few moments for the HDD to spin up and access the disk, so there is a bit of a delay, but only a few seconds.
I don't have Mario U on disk to compare any of the differences you asked about, but once the HDD is accessed and the start screen comes up, the game runs flawlessly.