A fun anecdote about the differences. My mom drives a Subaru Forester (from back when they were 2,500# rated) and had an 8 foot popup that she towed for years and got about 20 mpg. She recently traded it for a teardrop style trailer (T@G) that is basically an enclosed double bed with a kitchen available when you open the back hatch.
The weight is the same, just over 1,000#, but the T@G sticks up a few feet higher than the pup did (not enough to stand in). They get 14mpg pulling that from a little 2.5 liter 4 banger engine. And this IS a fairly aerodynamic trailer with a sloping back end. The point is that higher trailers push more air and require a LOT more engine power.
In the end, it's your decision. I love minivans and think they're ideal popup tow vehicles and I've done that for tens of thousands of miles. But I'd not tow a full height RV trailer with one. Just not enough margin left.