I prefer tanking on my Monk to my zerker (both mythicalled) tbh unless it's one of the Guk zones

Brawlers really do have to fight to keep aggro with multiple mob encounters, so getting your targetting keys sorted is a must. My gear is pretty crap tbh, with the majority being T1, but I still use the juggernaut skullcap for the 5% avoidance for tanking.
I have 3 gear setups, tanking, mid and dps. DPS I'll never use when tanking due to items like ring of animosity, but while tanking I'll try to use mid as much as possible for aggro.
I have 2 AA spec's, one solely focussed on tanking, the other a hybrid. Dodge and weave, tsunami, mountain and stone stance all increase our survivability a tremendous amount, and tbh, with decent dps, heroic mobs should be down before these are used up.
As mentioned above, shammy's are perfect for brawlers as mitigation doesn't count for damage taken by wards.
As far as epics are concerned, I had no problem with survivability or aggro with tanking PotAO trash and the 1st named(s) with my crappy gear - yes they are pretty gimp mobs, but hey-ho, gotta start somewhere!. The key is using what skills you have to the max. Trash was mid stance, and named were defensive stance. Trash did sometimes involve multiple encounters, which needed to be locked down - peel is great for locking them down while you concentrate on other mob. Aggro wasn't a problem with only a couple of player deaths, too much dps on incoming and a spike.
Once I get my gear up to T3/T4, I'll hopefully be on the bigger stuff!
I've just joined a guild where I'm fortunate enough to have my monk as main again (been 2 yrs), so he's always been low down in the pecking order for shards. The joy of shard farming again!