Without a doubt, Ashley is more annoying. I know that she dosen't get killed as much as Sheva, but when you break it down to the cold hard facts there is no denying that Ashley is more terrible. She can't punch, she can't kick, she can't shoot, she can even tell who is an enemy or not. To also add on how sad she is, she is about 18 in the game. You can not tell me that she couldn't know how to use a gun at that age since there was a RE character (Rebecca Chambers) who was 18 and did use a gun. It is just simple to use a gun, just point, aim pull the triger, reload the gun, and don't aim it at yourself or your friend. I don't care if you say that Rebecca could have use one because she had traing, but Leon could have said "Ashley I am going to teach you how to use this gun. Just *explains* and that is it. Now this mission can become easier." Lets also mention how she will just stand right next to a Ganado, Zealot, or whoever, but if someone is going to kidnap you and/or kill you there is a thing that you can do to avoid it. I think it is called running away.
So overall, Ashley is the worst out of Sheva and Ashley.