Both would be BRILLIANT choices but Emma's amazing ability in Harry Potter to play a powerful, skilled character and do action scenes so flawlessly makes her a perfect choice. Either of them would be amazing for the part of Batgirl/Barbara Gordon because they are amazing actresses, have played badass characters with quick wits, and are absolutely attractive (especially Watson).

Both would be absolutely PERFECT casting! Both have played characters (Hermione Granger and Gwen Stacy) that are highly intelligent and have solved many obstacles with their brains, which is an important quality of Barbra Gordon/Batgirl, since her intelligence served as an important asset when she became The Oracle after becoming paralyzed from the waist down. They also have amazing acting talent, can be absolutely badass, and are attractive as well. But I feel like Watson would be a better choice because I think she's a better actress, though I would be just as happy with Stone as well.

I would find both equally boring.

I hope they give the opportunity to a lesser known actress or newcomer.

Eh, I don't think they both fits with that character...