PA mids are more sensitive than conventional mids and thus, louder. The tradeoff is that they aren't as user friendly with respect to sound quality in poor enclosures.
Since doors are the most common enclosure, I'll focus on them. With conventional mids, you will get a little better SQ without as much (or any) work on deadening and sealing your doors but you also won't get as loud or as clear a sound stage. With a properly deadened and sealed door, PA mids can provide intense sound pressure and very good midbass response at higher volumes on the same power.
PA tweets are just loud. You can tame them a bit with higher crossover points but if you're not building an SPL only system, I would avoid them. They generally have metal pistons and that translates to harsh but loud treble so they're not well suited for sound quality oriented builds.
If you're building an SQL system you can mix PA mids with conventional dome tweets and end up with a really nice sounding loud setup but again, door treatments are a must with PA mids.