The mini will be quieter. BUT, most minis don't have backup heat so if a cold area, the heat pump alone may not cut it. The 5500 (and newer 5800) have up to 5kw backup. They are the quietest PTHPs I've heard.
Installation costs will be higher with the mini. All the PTHP needs is an outlet and a hole in the wall.
Has someone done a heat gain calc to be sure 12K will do it?