Well I'm a monk main and not a dragoon main, but you shouldn't have any problem maining Dragoon as a DPS. The closer the fight is to a punching bag the easier it will be for monks to out DPS you, but in fights with several pauses where monks can't keep DPSing thus causing them to lose greased lightning dragoons will be able to hold the higher damage. Aside from that dragoons have a much easier time AoEing than monks do and have much better spike damage when you need to burn something quick.
On an end game perspective Monks and Dragoons are fairly even, only problem being that they are often competing for the same spot as melee dps are less favored in a lot of content.

Blms are the kings of AoE, and just got a boost in their single target abilities so still good there. Only downside is their lack of mobility for their long cast times. Overall it shouldn't be hard to find a spot if you like blm. Smn is similar, and fits more roles but they are more of the "jack of all trades, masters of none" job. The nice thing is they share a lot of the same end game gear, so just get weapons and you can "main" both easily enough.

Bards due to their nature will have a spot in everything, but there is a huge player base of bards already so if you don't like it yourself there's no need for you to play one ^^