Yes, Apache on windows is probably a better environment for PHP/MySQL than IIS. If for no other reasons than the lower number of serious remote root exploits and the numbers of days (weeks, months, years??? ;) they live for on IIS versus apache.
But, Linux is probably a better performer overall in terms of reliability and speed when running multiple services on an app server like that.
When moving from one platform to another, it's always a very good idea to dump and restore your database with the tools supplied by the developers and all.
Linux is pretty easy once you get the hang of it. Expect it to take a week or two for you to get a feel for it, then you're off. Look for a mentor if you have to switch OSes, it's much easier if you have a buddy with a Linux clue when you're trying to figure out how to do stuff.