MNK:
+ very fast paced and mobile class which makes the play style dynamic and engaging. Best single target DPS but under very strict conditions.
+ You'll get a lot of loot because you'll usually be the only melee, DRG and MNK don't share gear like Casters, Healers or Tanks, and somehow RNG seems to like MNK. I personnaly lvled a monk because I got all the Allagan gear and accessories from running Coil as Tank.
- A monk will only do amazing DPS in ideal situations where they always have clear access to rear/side and can keep up their greased lightning stacks up all the time. Unfortunately, their are too many fights that aren't monk friendly... In most fights, a MNK won't be able to pull that much ahead of BRD because they have much more uptime. You'll only be a DPS star on a training dummy ...
- Monk has no utility to the group other than it's single target DPS and LB
- Monk has position requirements on all attacks which makes them terrible at soloing. for example, my WAR does more DPS than my MNK when doing Beastmen quests...
- Monk are bad at AOE and Bursts. They can be good but only if you have Perfect Balance available (which has a ridiculous CD time I find).
- Groups won't need you... pretty much all fights are better done with range DPS and if you need to bring a melee, DRG is better overall because of their Burst, piercing debuff, LB, and more consistent DPS (because of less buffs and dots to maintain).

BRD:
+ Amazing utility to the group, people always want a BRD in the group.
+ Amazing DPS overall because of the uptime and no positioning requirement
+ Very good Aoe and burst DPS
+ You'll get a lot of loot as well because gear and accessories are specific to BRD and you ain't competing with any other class on loot.
- There are too many BRDs out there, so you'll fight for loots since it's not unusual to have 2 BRDS
- You'll have very bad queue times on DF
- I can't see any really, unless you just don't like the class