Say something like Eruption. Let's get past the "why would you waste your time learning that..." As guitar players, it is at least something most of us are familiar with.
Would you learn the entire piece in it's entirety at a slower speed and then work on getting the entire thing up to speed. Or, would you slow it down or would you break it up into 4-5 sections and work on getting one section up to speed before moving on to the next?
I tend to sort of do both. Then eventually I get the entire piece together and work on getting it up to speed. Of course, I am playing a variety of things (new and old) at the same time so it can take longer than it would if I was just focusing on one thing at a time.