The things I look for in an ABA are:
Somewhat dry, but complex, American malt body with a fair bit of light to medium toast notes - nuts, bread crust, biscuits and crackers - with very restrained dark roast - light chocolate, cocoa powder.
Neutral yeast character, with restrained "tree fruit" esters - maybe some apple, pear, or fresh plum or cherry. If they're up in the moderate range, they should reinforce the hops, not the malt.
The beer can have some heft to the body, but it should be dextrinous fullness rather than underattenuated sweetness.
Malt to hop balance can go either way, but should be reasonably well balanced. Too much hop bitter will clash with the dark malts and give the impression of astringency; it's a real trick to brew a good hoppy dark beer. Thinner body and high hop bitterness turns the beer into a "Texas Brown Ale"/"Brown IPA." Fuller, sweeter body and lower hop bitter turns it more towards a Brown or Robust Porter.
On top of the hop bitter and malt complexity, there should also be some late hop character. It's usually citrusy and piny, but doesn't need to be. Too many judges forget that.
BJCP Style guidelines specify low to moderate hop aroma and flavor, but I think that lower hopping levels tend to throw the beer towards being a porter unless the brewer works hard to get a lot of "brown ale" character into the beer and brings up the hop bitterness.
On the other hand, I think that too much hop flavor and aroma also tends to clash with the dark malts, so it shouldn't be too over the top. But you still need a some late hopping to remind the judges that the beer is a brown ale, not a porter.
Since I'm sort of on the East Coast, I see more balanced versions, and for commercial examples I think of Brooklyn Brown Ale, Smuttynose Old Brown Dog and Avery Ellie’s Brown Ale (Yes, the 2008 BJCP Guidelines turned it into a Northern English Brown, but I think that the Guidelines committee got a bad bottle.)
For more aggressive "West Coast" versions, I think of Clown Shoes Brown Angel, but it's a bit high in alcohol for the style at 7% ABV.
Commercially, I think that the trend was towards more balanced versions, but now it's swinging back towards more aggressively hopped beers. That might also be the case for HB, but I haven't brewed or tasted an ABA recently - it's the rarest of the American ales.
As to Peter's beer, my ignorant guess is that the judges got a fair bit of bitter and citrusy hops in the flavor, but it didn't carry into the aroma, or vice-versa. Judges often like to aroma and flavor to be similar in intensity. In particular, it sucks when a beer has an amazing bouquet but the flavor doesn't follow through.