In my opinion, a "Parabolic softbox"....really is a contradictio in terminis....a contradiction in terms.
A softbox is meant to scatter light around. A parabolic reflector reflects light in a specific direction (and can be used as a softbox by using diffusions/cloth/anything)
So, I think a parabolic reflector can be used as a softbox if you wanted to, but a softbox can never be used as a true parabolic reflector.
I don' t trust any company that advertise light shapers as parabolic softboxes.
In my opinion (only based on user reports/review/internet information), there are a few major brands for Parabolic light shapers:
Broncolor / Briese / Parabolix.
The first 2 are probably the best money can buy, but also the most expensive options. Parabolix comes VERY close in results for a fraction of the price.
Luis Gabriel did a very good review on FM a couple of months ago. Worth reading/watching.
www.fredmiranda.com/forum/topic/1760509
As a beginner in studio lighting/ studio photography with strobes, I also posted on the DPR forum (about this subject). Might be interesting as well:
dprforum.com/community/threads/first-one-here-more-please.515/