For club foot animals like a coyote the offset jaws allow the levers to ride up higher on the trap due to the gap....thus in theory creating a better lockup. I don't know that it really matters but if you catch someone's dog the risk of foot damage will be lower with offset so either of those is a good enough reason for me to use them.

For beaver and the like I use close jaws on drowner rigs which I rarely use anyway. Think about the shape of the foot. Generally I think if the animal has a tapered or really small foot I also use closed or standard jaws for things like Muskrat, Coon, etc.