As far as melee rankings go it's: MNK > DRG >NIN
MNK/NIN mobility verse every other Job's mobility is barely noticeable when it matters, what is it 10%? Simply Sprinting (no cost) puts everyone on the same pace. The additional movement speed is one of the few one-ups NIN has over DRG, which is barely anything if you are trying to catch-up. Which is not really an issue with numerous gap closers/weapon throw/sprint/cc/etc. In the escape options, yes its a plus, but that is about the only avenue NIN has over both MNK/DRG.
MNK is superior when it comes to defense and defensive utility, hands down. NIN's Shadeshift is also fairly powerful, although it only works against Physical Attacks. MNK/DRG have Bloodbath, which is exceptionally powerful to help heal themselves if they are getting bursted while they are bursting, in which Life Surge also has additional healing. Bloodbath/Life Surge + Enhanced Keen Flurry vs Shade Shift puts DRG/NIN pretty even in the defense department
The enhanced movement is only valid when you are escaping thus meaning you are most likely on the losing end of the encounter and/or sacrificing damage to potentially alleviate/delay yourself of death. In the theory of using the movement speed to escape, you are also saving Fetter Ward for it, any decent player/team will use Stun/Heavy/Bind to catch-up and demolish you, and if you are saving it for that, that means the burst you may do will easily be interrupted.
Monk's utility is so great because of its uniqueness, the ability to repeatedly strip buffs, enhanced Mantra, AoE Pacification, and the bonus of reducing caster damage.
NIN on the other hand has a Bind (EVERY Range/Healer has this,DRs), Grounded Heavy (sacrifices damage to do utility ninjutsu), a 3s silence (very good), 10% vuln (unreliable), slashing debuff (lol PLD damage), and the ability to Hide (which is more of an oversight than utility). The utility that stood out the most for NIN was taken completely away, which was the 20% healing down.
NIN's utility on paper seems like a lot, but take it in to an actual Lv. 60 PvP fight, and the power it once had in Patch ~3.1 Lv. 50 Den just feels so weak in comparison.
DRG's utility is mostly damage boosting with Disembowel and Battle Litany which are very strong. Battle Litany being good for offense/defense allowing healers to crit more. However DRG has taken a hit to Slow/skewer duration, albeit, the slow is still exceptionally strong.
DRG/MNK also very slightly increase tank damage just by existing in the party.
DRG actually has a lot going for it. On top of the stuff mentioned above, it has the strongest burst of the three which is saying a lot in a game mode with win conditions centered around strongly timed burst. While NIN burst is not far behind, it is unreliable, and can be seen MILES away, more noticeable than that of a Bard. It is also easier to mitigate by simply not turning your back to them forcing them to blow a stun if they think they're gonna do a powerful burst.
Overall(NIN/DRG): DRG has superior offense/sustain, NIN/DRG similar levels of defense, NIN better utility, DRG has superior burst. DRG is just simply better.
Being able to run and hide like a b- is the only reason to bring a NIN, but it doesn't make a job good in a game mode about killing other players. Unless, of course, we are referring to solo queue in which no one knows anything about Ninja.
Even then, in order to get out of combat you have to either kill everyone or be almost 65% of the map away from the people you are in combat with. Yes, if by some miracle your team gets ahead of another equally skilled team (different comp), perhaps you can run for 3 minutes around the map. I'd just bring a BLM for that though.
Don't get me wrong, though, I adore Ninja, would love to play it again competitively, but it just isn't there.