He also brings up another good point, however: in terms of class balance, Arenas are a much more striking example of imbalances than battlegrounds are. Battlegrounds have all sorts of things going on, and so you don't get as good a picture of just how the different classes work with and against each other as you do in Arenas. And so, if you're a dev trying to figure out class balances, of course you'll spend more time looking at the Arena gameplay than the BGs. GC also says that the majority of issues in BGs tend to be map-based rather than class imbalances, which is really a whole other science. Not that BGs aren't relevant to how the classes work, just that there are many more variables in there than the relative vacuum chamber of Arenas.
All good points. I'm a fan of battlegrounds much more than Arenas, but I don't particularly feel that Blizzard has ignored them necessarily. The real problem, to my mind, with BGs is simply how faction imbalanced they are: it seems like on every realm in every given BG, one side always seems to have the upper hand, for whatever reason. Sometimes it's a population problem, sometimes it's a map issue. But GC is right: those problems are more pressing than class balance in the BGs.