Cherche or Michalis

Cherche, especially +atk, is a really good unit when given a brave axe. I think she is generally considered to outperform Michalis. Both are good units though, so it can come down to whether you want a decently high damage flying tank, or a flying glass canon. I've seen Michalis compared to Hector and Cherche is somewhat comparable to effie in damage.

Cherche. She has the highest attack of any green axe flyer and only has 3 points less in defense, she'd take a bit more investment if you're going for Brave Axe build whereas Michalis can keep a lot of what's in his kit.

Better question is why wouldn’t you use the 2nd best Awakening girl over a murderer :P

In all seriousness, I recommend Cherche. Fantastic offensive unit in and out of Flier Emblem. Not that Michalis is bad by any means, but he doesn’t do as well outside Flier Emblem from my experience.