They're both relatively similar. From a mechanical standpoint, Monks attack faster, have more rapidly switching positionals, and have better team-based defensive utility (traited Mantra). Dragoons attack more slowly, have more off-GCD abilities to interleave, and have better offensive utility (Disemowel debuff). Dragoons also have slightly more mobility (second gap closer; Monk only has 1).

Monks have a bit higher magic defense, Dragoons have higher physical defense.

Dragoons lose moderate DPS if they can't use Leg Sweep (the stun) due to diminishing returns conflict with stun interrupts. Monks lose moderate DPS if they disengage for 10 seconds every time they disengage for 10 seconds.

Dragoons lose significant DPS if they can't attack from behind (AK Demon Wall); this situation is rare.

Both the MNK and DRG high-DPS attack sequences are more or less equally complex / not-complex depending on your perspective and experience.