coming from somebody who used to parse religiously with basically maxed gear, faith will beat destroyers easily.
This is at G. colibri camp, clearing all mobs (both before they changed the mobs and after, we cleared it regardless). I used to often xp with another maxed mnk (we both used our own outside PLs/hasters, and always partied with 2+(heh) bards)
if I had to afk to bio or whatever, I'd throw on faith after until I was ahead in the parse again. They would steadily overtake destroyers all other things being equal. (assumes capped accuracy on both mnks)
this is all a while ago, so some gear has changed. Usually double march, double attack for brd songs. spamming sushi like we were starving

(if I'm under 85% accuracy in parse, I spam sushi, gtfo meat eating mnks a couple years ago) with full salvage gear, meat is probably better, but before that, dreaaaaaammmmm on.
unfortunately the only mnk I ever parsed against with relic was always geared for lowman/endgame, but I'd bet for merit situations faith beat relic.