Cheshire Vs Ra's al Ghul

Winner? Cheshire or Ra's? 
This battle will be inside of a Japanese Dojo. Ra's is in character. Cheshire is out of character. Ra's has  a katana sword. Cheshire has her katana.  The fight is to the death. They face to face, of course. Recent Versions of them. Who wins? 
 

 
 
 
 
 

I'm going with Ra's here. He's probably the better sword fighter.

Close, but I'd give R'as the slight edge.

@CosmicCupcake said:

Winner? Cheshire or Ra's?
This battle will be inside of a Japanese Dojo. Ra's is in character. Cheshire is out of character. Ra's has a katana sword. Cheshire has her katana. The fight is to the death. They face to face, of course. Recent Versions of them. Who wins?

In what way is Cheshire "out of character"?. You can't make an open statement like that without explanation. This could mean anything.

@Void_Paladin said:

I'm going with Ra's here. He's probably the better sword fighter.

Ra's wipes the floor with her in a sword fight.