What is the difference? When only one of einfachheitshalber and der Einfachheit halber fits?
The word einfachheitshalber is an adverb made from the preposition halber (meaning: because of) and the noun die Einfachheit. There are some more common adverbs of that sort:
The phrase der Einfachheit halber is just the expanded form with the exact same meaning. It's preferred if the noun is rather long or already an aggregate, and die Einfachheit is.