How are monks compared to dragoons?

in term of survivability and damage?

Superior MNK damage hinges on a target's elemental weaknesses.

Given an otherwise level playing field:
If a MNK fist can exploit a weakness, MNK will always do more damage than DRG.
If a MNK fist cannot exploit a weakness, DRG will always do more damage than MNK.

In terms of survivability, they are about equal. Same HP rating, same defensive capability. MNK gets more HP from Second Wind, but DRG gets additional HP from Dread Spike. Most DRGs would rather die than give up Power Surge, though. (*'-')

They are pretty equal in comparison. I think someone who wants to main DDs should have both. A good example would be like Miser fight vs. Moogle fight where Monk can use Fists of Fire and wreck Miser and DRGs probabl have the highest dps in moogle. Typically DRGs are preferred in Primals and MNKs in dungeons.

What are these monks and dragoons you speak of?

Only classes I've seen are warriors and black mages.

Everything else is a novelty.