I spent a couple hours last night in the new HS Battleground, an 8-player game mode that is most similar to the "chess" style of Brawls. I found it quite enjoyable, playing something like 6-8 rounds. There are some glaring flaws (like wildly unbalanced hero powers) but it's still in Beta and I expect at least one round of balance changes before it goes live.
The set of cards presently available is also quite limited, leading to a very small set of "armies" you can build, with some clear winners. Pogos rule, if you can get the RNG to give them to you. I assume they'll expand the card pool as it moves toward release so there are more potential things you can do.
The biggest downside, beyond the balance problems, is the immense effect of RNG. Drafting (building your army) is dependent on getting triples of your chosen minions and if Bob doesn't offer you what you need then your power level stalls out while people who get the right choices will curve past you very fast.
Minions attack left-to-right and respect taunt, so you have some control over things but choice of targets beyond that is random and can have a huge effect. Modifiers like poisonous and divine shield can be overwhelming if the RNG falls in your favor or nearly useless if it does not. It's not clear to me how they can deal with this; maybe they won't and just over time your RNG will even out. But it still feels terrible to have a set-up that ought to win and uncontrollable RNG screws you.