When my outside cats are full they don't hunt as seriously as they do if they are hungry. The chasing is more for sport and practice. Save the tasty critter for when you are hungry. So she may not have been going after it full throttle. When my guys are hungry they barely even play with their catch. Its just dead and eat and done.
Maybe she is thinking that you are scaring her prey off OR she might feel that your competing with her for prey.
Maybe she is thinking that you are scaring her prey off OR she might feel that your competing with her for prey.