I've got both, inherited from my parents. Just something about the Morgan that seems more pleasant to the eye.
I think it is the amount of detail on the Morgan that makes it better. With such a big silver coin to work with, I just think they could have come up with something better, possibly more intricate for the Peace dollar.
The morgan does have a lot of detail...And the thing that just makes me stop, in total awe, are the hair lines on the coin