I've decided to upload a video showing how real the eDPS issue is for Demon Hunter's at higher Monster Power.
For this video I recorded runs of both DH and Monk, wearing 9 pieces of the same gear. The different pieces were: different SoJ for each class, Skorn instead of Manti/DML, and Inna's Radiance instead of Mempo. Basically even if there is a gearing difference, it isn't that major.
I've also made sure the situation was already IDEAL for DH DPS, where I got an elite with Mortar so it's standing on spike traps the entire time. Had the mob actually moved, things could have turned out much worse for my DH.
The DH has a higher pDPS (paper DPS, what you see on the character screen), yet the difference in ACTUAL kill speed may be larger than you'd expect.
Basically the Demon Hunter's pDPS should be closer to it's eDPS. With nearly the same gear, it gets higher pDPS, making the class look fine/competitive, yet at the end the eDPS turns out to be significantly lower than other classes.
Edit: Here is the extent you have to degrade your weapon to match a Demon Hunter's low eDPS. And even with such a lowered pDPS, the results vs non-stationary mobs would still be in the monk's favor, simply because spike traps (the current highest eDPS ability for DH) lose effectiveness vs mobs that move.
And for those wondering, Monk is not overpowered. The other classes (Barb/Wizard) can both get similar pDPS to eDPS results. I can't comment on WD's as I've never played with one, and hardly ever played with any in Co-op games.