Well, like others have said, it depends on the fight.

Although, since you asked for the highest DPS, the answer is simple, DRG...

In different fights, the DPS will vary between the jobs, but on a single target, the DPS can never be higher than a DRG in a perfect scenario.

Alex(normal) is pretty forgiving for melee DPS, so they should be on top, but we don't know how the mechanics will work exactly in Alex(Savage), where it really matters.

It should be mentioned though, that DRG's new rotation that gives them that high DPS, doesn't work in many cases, and you have to hold on to skills to not lose even more DPS. MNK on the other side, doesn't use much of their new abilities unless there are some mechanics to dodge etc, and NIN just doesn't get as affected by mechanics as MNK and DRG. So unless you know you have 100% up-time on a boss (even Alex F4 can screw a DRG with getting sucked away), DRG lose some of that DPS advantage, MNK will gain some relative DPS, and NIN just adapts to some fights better and keeps much of their DPS. Overall, all melee are pretty close in real fights and striking dummies never tells the whole story.

In very specific fights where melee gets screwed while ranged can stand still (and I mean really still) for a long periods of time, BLM is the winner, but usually in raids(not accounting for AoE), melee DPS jobs are on top, so if you're interesting in highest DPS, look at melee... At least if they keep the trend they've had now with FCoB and Alex(assuming savage doesn't change it completely).