Against a dummy, seems like DRG, NIN and MNK are all very close to each other with BLM/SMN pretty close behind. My guess would be BRD and MCH have closed the gap some as well (though not sure we have parses of it yet).

On fights with high uptime and low melee mechanics (A4) the melee DPS with higher skill will likely win (from my parses anyway).

If a fight allows BLM to turret and there are melee mechanics, they probably win. If there are melee mechanics AND ranged ones, SMN will win followed by MCH and BRD most likely as they can continue DPSing safely.

Most of this is speculation but really it ends up coming down to individual fights.