Curiosity got the better of me and I tried my hand at some DPR math. It includes the crit chance, but I didn't do two-weapon fighting for the rogue and I hadn't figured out how to add Advantage yet (in the case of Steady Aim).
Rogue 15
+1 dagger, +11 to hit, 1d4+6+8d6 avg. 27.375
+3 rapier, +13 to hit, 1d8+8+8d6 avg. 34.425
Monk 15
Staff of Striking +13,+13 to hit, 1d8+8 avg. 21.25
w/ Unarmed +10 to hit, 1d8+5 avg. (7.6) 28.85
w/ Flurry +10, +10 to hit, 1d8+5 avg. (15.2) 36.45
The monk is definitely doing well compared to a rogue with an inferior weapon, but that isn't really very impressive. So I also included a line with the rogue using a +3 rapier. Compared to that the monk only surpasses it by using Flurry of Blows. I will also restate as others have that the monk can move some of his damage to another target if their current target drops, whereas the Rogue just wastes their damage on overkill. This is also just using Flurry of Blows. If the monk can land a Stunning Strike his DPS jumps massively.
Speaking of Stunning Strike. When ever it is mentioned as being crowd control the caster with Hypnotic Pattern is mentioned. So I went ahead and calculated the DPS of a Wizard using Hypnotic Pattern.
Wizard 15 w/ Hypnotic Pattern DPS avg. 0
Wow! Look at that! The monk just blows him out of the water on DPS.

I would also like to mention that while the monk can stun 1 creature per hit, the rogue stuns 0. So the monk wins there as well.