Guessing you used Chaos. I'll use Final Omega since it's 100% potential uptime.

99th Black Mage: 9100
99th Red Mage: 8,000

Difference: 1100
% difference: Favoring Black Mage by 13%

Using Voidwalker since it also has potential 100% uptime

QUICK PRIMER
RDPS = The damage that 'belongs' to the job in question.
ADPS = The damage that the Job conveyed to the boss, minus single target buffs (Dance partner, Eye, etc)

ADPS

99th Black Mage aDPS: 15,292
99th Red mage aDPS: 12,576

Difference: About 2700
% difference: Favoring Black Mage by 21%.

RDPS

99th Black Mage rDPS: 14,922
99th Red mage rDPS: 12,883

Difference: About 2100
% difference: Favoring Black Mage by 15%