I don't suspect that disk access times has anything to do with compilation times as all the code (compiler and sketch) are already in RAM before compilation starts (except, maybe the libraries that have to be reloaded in case thay have been changed in the meantime).
You may have noticed that the first time a sketch is compiled it takes a lot longer than the subsequent times (when you only made changes to the sketch. The message that the IDE sends is that the compilation values have changed, and that it has to start all over again. (I am just translating here since I use the french IDE).
I woundn't expect a big change in compile time with the change of your computer. If you run a benchmark test on both computers, you might find that only 5 to 10% increase in processing power (and/or speed) That would make a 60 seconds compile time to drop to 55, 50 seconds. Nothing to be really noticable.
Jacques
EDIT : just checked with userbenchmark.com, and you new processor should be more than 2 times as fast...