Open *generally* means with no syllabus restrictions, but it can also mean "open to all comers", as in the difference between the US Open and the US National titles. But anyway, I know you're talking about the first meaning here.
In Pro/Am there are the somewhat oxymoronic (interesting word choice there....) divisions "Open Bronze, Open Silver, and Open Gold." The way it's always been described to me is that if you are in Open Bronze you may incorporate Silver steps into your competition dancing, and if you are in Open Silver you may incorporate some Gold, and in Open Gold you can start using some of the common out-of-syllabus "named variations."
Open (as in out of syllabus, not what I just talked about with regards to Pro/Am) is more popular because it has more status and cachet. If you're in amateur, you finally get to wear costumes. No matter who you are, you finally get to start doing some of the "flashy" stuff. No doubt about it, being able to dance in open (as in out of syllabus) is the cherry on the ice cream sundae that is dancesport.