Never tried a swede saw yet, but I am sure they just as good.
The bow saw / swede saw / buck saw or whatever you call it works on the principle that the blade is allways PULLED through the material. Pushing a saw blade you risk that the blade folds and breaks - all it takes is that the blade gets stuck just a tiny bit and you start bending. Pulling a saw blade is much better. Try pushing a rope, you'll see pretty quickly why pulling is a much more mechanical robust way of doing things.
A saw blade made without an external frame (such as the gerber folding saw) must be very rigid and stiff to prevent it from bending when you push it forward. A saw blade made for a frame (buck/swede/bow whatever you call it) can be very thin and still plenty strong enough for the task.
The drawback is that the external frame may get in the way. There are certain tight spots you can't move the frame into, and can't work a good stroke. In those tight spots only a thin, rigid saw blade (your Gerber friend) will work. Also, the thickness of the material you cut is limited not only by the blade length but also by the shape and size of the bow. Also, the bow is somewhat more complicated to pack and assemble than your Gerber saw.
The plus side is that the thin blade offers less resistance than a thick blade. Also, the blade can be made much longer than their frame-less friends. And since you don't have to worry about the blade folding you can work with really long, powerful strokes.
A big swede saw is a true joy to work with - and in my opinion, the most efficient manual saw there is. A carpenters saw will give you more precise cuts. A small folding saw (Gerber) will be better in tight corners. But no other saw will give you more firewood per calorie or time. (Of course, that's assuming you get a good blade with big teeth of the right shape).