In my opinion, the main factor to consider would be power output.
Many ring flashes are only suitable for close up and macro photography because the original premise was that your camera and you would cast shadows. So the power will probably not be enough when you step back and try to use it on a full body portrait.
Regarding the size, I would assume, as with all modifiers, the larger the softer. But I doubt the difference is very noticeable, as you do not have directional light, but you probably will notice it on the halo-shadow projected behind the subject.
One interesting option is the softboxes that act as a ring flash using a normal speedlight. They are lens-independent.
And you can use them as an off-camera softbox too.