With the current mechanics and content in the game, MNKs are probably slightly more effective than DRGs for a few specific fringe reasons:

1. They do higher single target DPS. DRG AOE DPS is useful, but BLMs are also pretty common, and can sufficiently fill whatever AOE needs are there.

2. They have a few bits of pretty unique utility that DRGs don't have, like the %Int debuff in their rotation as well as the traited Mantra increased healing.

The main DRG utility benefits are the piercing debuff for Bards (who are a slightly behind in DPS in the first place), and the ability to tank some stuff a bit better, which doesn't matter much. DRG's also have slightly higher controllable burst damage, which has its uses.

Overall it's kind of a wash, but MNKs are more effective by a slight measure.