I have by no means played both at endgame, but here are my two cents. Dragoon is a bit slower and more bursty and will melt trash and adds like they are nothing. Monk on the other hand because of its ramp up wont be as helpful on trash and adds however a good monk will come out on top on boss fights followed by a good dragoon. what most people dont understand is that they are inherently different. and it really comes down to preference. I personally chose dragoon simply because my FC has quite a few monks and I really only play melee and we also have plenty of tanks.

TLDR they are different Dragoon= BURST Monk= SUSTAINED both are a lot of fun, but that is subjective.