Battle.net client is in public beta now, got in installed when I launched Diablo 3 to update it. It basically is as, if not more, limited as Steam was when it first launched. You just have a Games tab, which you can't even filter to limit to games you have installed (like that WoW trial I tried once or Hearthstone which I have no interest in trying), and a News tab. The Battle.net client is super, super basic right now. I'd even put it behind the Origin and uPlay's clients because they at least have limited stores and social features, like friend lists.
At least Battle.net will auto-patch your games when launched, which is nice, but man do they have a loooooong way to go to catch up to even Origin and uPlay, never mind Steam.