Ana is very interesting in design.
She has the potential to heal more than mercy, although a bit tough to pull off, you just have to hit all 8 of your shots. The grenade may double healing done, but you're not likely gonna get all your shots to land on your teammates during an engagement. You might even miss all your shots if you're really bad (although I've heard on PTR that the hitbox for allies is very generous). I'd say she's more of a utility oriented support. The kit she brings makes it that she can help offense big time. Make her team survive a bit more or make them kill a bit faster. The sleep gun is cool in concept, it would be interesting to see what kind of cool combination plays people pull off once we get used to the whole sleep mechanic.
Another thing to consider is that Ana has no mobility skills. Meaning she can't get to a good position(in most maps) where she can keep track of her teammates and her enemies. and with a pathetic hp of 200 and no shields/armor, a good Widow/Hanzo will completely shut her down. Ana players will most likely be at the very back of the team instead of some nice sniping spot like the hero preview thing makes it look to be. She also has no big team saving abjility. (like Mercy's revive, Zenyatta's transcendence, or Lucio's everything)
TL;DR She's a solid secondary support that can temporarily make one teammate into a god.
Edit: So apparently, her ultimate charges really quickly, like Widowmaker levels quick. Meaning we can just keep turning our teamates into junkies as much as we like. cool.