Generally speaking, single speed folders are made for short commutes where someone (often in Europe where public transportation is utilized by a much larger segment of the population) rides the bike for a mile to the bus/train, folds it up and takes the bus/train, and then exits and rides the bike for another mile until they reach their destination.

Although you are probably going to take your bikes for short rides after reaching the campground that might be OK, but only if those areas are going to be flat. If you are going to ride in hilly areas, you'll want geared bikes. Plus, there may be areas just outside the campgrounds that you may want to go, and those could be places where you don't want to drive to, but could be longer or "hilly-er" than what you would want ride on a single speed folder. Unless you know exactly the distances and changes of elevation of every place you will be camping, a geared folding bike will allow for those types of variables without sacrificing the ride like it may on a single speed.

Single speeds tend to be lighter in weight and fold flatter than geared folding bikes, but the benefits of a geared bike may outweigh those factors, no pun intended.

Between the Gotham and the Miami, I'd buy the Miami because it has fenders. If you've ever ridden a bike right after it rains, or there are puddles in the road, you'd know why this is important.