Don't discount the value of having doors that slide back rather than folding forward, both for how much opening you get into the back, and for how easy it is in parking spaces. Additionally, that extra height is extra height that every bag or child has to be lifted.
Also, I think my parents' minivans turn tighter than my wife's full-size sedan (Impala). I understand that the most important thing is how it compares to the handling of your current ride, but what I'm trying to say is that a minivan is still quite a few steps down the food chain from the enormous vehicles that they design roadway geometry around (enormous American firetrucks, typically,) so you'll have some wiggle room either way.
In any case, I think you're likely to have the minuscule difference in fuel efficiency dwarfed by a difference in purchase price, throwing the baby out with the bath water. At the end of the day, those vehicles are all thirsty because they're enormous bodies with even more enormous engines.]
I'll look at 2014 cars:
To try the numbers, I looked for a list of 'efficient' 3-row SUVs (with 4WD), and found the Toyota Highlander hybrid (27/28, 3.6 gal/100mi, goes back to 2014),Mitubishi Outlander (24/29,3.8gal/100mi, reviewers dislike the third row and this is a 4 cylinder model), Nissan Pathfinder hybrid (same numbers as Mitsubishi)
Toyota SUV (27/28, 3.6 gal/100 mi): 360 gal per 10kMi (baseline) (added cost at $2/$3/$4)
Mitsubishi/Nissan SUV (24/29, 3.8 gal/100mi): 380 gal per 10kMi (+20 gal) ( $40/60/80)
Toyota Sienna AWD (16/23, 5.3gal/100mi): 530 gal per 10kMi (+170 gal) ($340/510/680)
Honda minivan: 19/28, 4.5 gal/100mi 450 gal per 10 kMi (+90 gal) ($180/270/360)
Obviously, double those numbers if you drive the family car 20kMi per year. This assumes you drive at the same efficiency and profile of driving types as the EPA does, but it's a start. And what I'm trying to show is that the gas difference may not be the difference you think, compared to finding a good deal on whichever vehicle you choose. I used 2014 because that's so new I don't think anyone could be too worried about maintenance.
I don't know about insurance considerations, but it's possible that one class is cheaper than the other. Finally, remember that those SUVs are HYBRIDS. For normal SUVs, you should assume SUVs are comparable to, or worse than, the worst minivans in terms of efficiency.
At the end of the day, I'd say that minivans are more functional, and a pretty solid choice, and sticking it to the big companies because car-makers love when you buy those high-margin SUVs. But if widening the field allows you to find a used car that you're happy with for a good price, that's the real way to come out ahead in car buying (doubly so in the excellent buyers market that seems to pervade the entire country right now.)