I'm starting to think Hawkgirl goes 5-5 with Martian Manhunter. It seems like Martian Manhunter players are finding the match up to be quite challenging as well (now before we consider this a matter of lack of match up experience I will explain more).
Hawkgirl seems to beat him up close for a variety of reasons:
1. Hawkgirl can full combo punish 1,1,2 one of his strings for frame advantage and an overhead mix up with wing evade 2 into full combo.
2. She easily blows up 2, 2, back 3 on reaction for full combo with her 6 frame jab or down 1.
3. All of Martian Manhunter's strings and specials that lead to big damage are easily punishable either due to being quite negative or having large gaps. He's generally a less safe character than her, while all of her launchers are safe as are her mix ups and specials so she can be more liberal up close than he can be overall.
His down 1 can compete with Hawkgirl's though and while their normals are relatively similar speed, her strings don't have as many faults as J'onn's and she doesn't have to worry about her launchers being unsafe.
Something else to note is that while orb set ups can stuff mace charge wake ups, you can at times trade with mace charge and it's a suitable trade.
He can zone and limit flight with teleport and MB pillars, but we're all familar with a match up this sounds similar to where flight is cut off, Doomsday that most consider to be 5-5. Now mind you Doomsday and Martian Manhunter are different characters of course, but my point is a solid ground based footsie game and patient Hawkgirl play and pressure can hang with him.
I've been playing it a lot lately from both sides and it's a chaotic match up, but it's also a lot of fun and feels different from most match ups in the game, I love match ups with Hawkgirl where she can't rely on trait, but can still hold her own really well.