Grip: The main purpose of an arrow puller is to increase the amount of grip you have over the arrow. An arrow puller with little grip will require a lot of hand strength to hold the arrow. This is especially important if you shoot a high draw weight.
Size/portability: Most archers wear their arrow puller on their quiver or belt. Therefore, you want this gear to be as lightweight and portable as possible.
Ease of use/speed: You don’t want to spend a lot of time getting the arrows out of the target. More elaborate and complicated arrow pullers will be less intuitive and less suitable for daily use.