Might be worth considering their offspecs also. Priest wears same gear for disc/shadow (except for helm and mb a trinket), so easy access to offspec. A monk would need two full sets for offspec. Know this ain't what you asking, but def worth considering.
In terms of strongest healer, my vote goes for monk. They have some insane healing output. I been facing Thalia(?), and priests are NOT keeping up with his heals. Less dmg than a priest, so in a team where dmg is sufficient I would take the mw no doubt. This also opens up for the playstyle question. Mw is more about the healing, where as priest you tend to dish out a bit more dmg.
I am no expert so do not read my post as the absolute truth.
Also, priest hands down the easiest to gear.