I’ve cleared all of this raid on both vengeance and brewmaster, enough offer a decent comparison of the two specs I main. Both are roughly the same ilevel, with experience on the same bosses.
For Emerald Nightmare, I started bosses on my DH and took my brewmaster on farm. Originally this was because I am far more comfortable on my monk and I wanted to force myself to learn my demon hunter. It ended up being handy because the way a DH times their AM can more easily apply to the way a monk applies AM than the other way around. I can learn to time my Demon Spikes around an event, and that maps to Ironskin Brew pretty well. In contrast, a brewmaster is much more flexible, and can potentially use Ironskin much more often than a DH could do with Demon Spikes.