I had a chance to test her out in the PTR last night. She's pretty fun to play, but she's kind of underpowered. Her rifle doesn't deal much damage and it doesn't heal much either. She seems more of a mid range fighter like Hanzo than a truly long range sniper like Widowmaker. Ana's grenade is pretty good. It heals allies and increases other healing sources as well as damaging enemies and temporarily preventing them from healing. Her tranquilizer is also pretty useful, giving Ana a chance to escape a pursuer or make an enemy vulnerable to attacks. Her ultimate is pretty great. It buffs one of your allies, increasing their movement speed, damage, and making them harder to kill. Put it on a tank and they're sure to destroy the enemy team.
Overall, I think she's a good addition, but feels a bit weak. Especially now that Zenyatta is going to be buffed, he'll fill the role of a long range healer better than Ana.
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I played a few games with her on the PTR yesterday. Awesome. Her damage is pretty crap but her heals are decent and sleeper dart is amazing. Watching a Genji get all excited with his little sword after he ults and putting him to sleep is hilarious. Same with Bastion that's guarding a point. Put him to sleep and have him sit there while our Reaper casually walked over, many giggles were had. Her ult is also a ton of fun. Fire it at a Genji or Pharah that's about to ult and watch them melt the opposite team. It renders Reinhardts shield practically useless against ults, they just melt it.