We've been sort of looking at a Fiat but not really sure that we'd want something that small. Ideally, we'd like a VW Golf TDI but there are varying reports that damage could be done to a 6-speed manual with a clutch. I think somebody at VW is misunderstanding and thinking we want to tow a 6-speed manual DSG with no clutch.
But anyway, from what we can tell and have been told, the Pop and the Lounge are exactly the same vehicle but with the Lounge having nicer trim and a larger option list. Their dimensions and capacities are identical according the the FIAT website.
I'm kind of thinking the same baseplate will work with the Lounge as is being used with the Pop. Maybe you can call Blue Ox or Roadmaster to make sure. If you are close to the Portland Oregon/Vancouver Washington area, you can always drop by the Roadmaster factory and get advice. They're really nice people.
Here are the images of the two directly from the FIAT website; the first being the Pop followed by the Lounge ...the main difference is the fog lights that are on the Lounge (maybe that's why the base plate bracket can't be installed? ...again, I would think Roadmaster or Blue Ox can advise you on that):