It really just comes down to player skill. DRG basically ride from burst phase to burst phase doing poke damage(no pun intended). MNK on the other hand has a ramping burst design where you are trying to build to your final combo to pull off an enlightened limit break followed by said combo. You should avoid using any burst if you are under horrid roar obviously, but don't forget riddle of earth is strong as hell for countering enemy burst. It pretty much will just come down to using stun riddle and gap closers to counter the range DRG can keep.

I suggest using OBS or Shadowplay to capture your gameplay and review what you did wrong. I did this a lot in season one of CC and it really helped me improve on playstyle.