I have one of each. The thornless one is much more vertical, less bushy.
When I pick them, I always get stabbed by the thorny one, never by the thornless one. I told my sister this was the easiest way to tell them apart.
Seriously, about the only thing I see is that the thornless one seems to be putting out a lot more flower buds than the thorny one. A commercial grower once told me that he felt that the thorny ones had better flavor, but I cannot tell much difference.