"Would a beckett with wider but shorter cylinders perform worse than a taller thinner one?"
I know this one. You have two variables here to consider. Tube diameter, and height. The height is going to vary the injector's relative height in comparison to the water level in the skimmer's main reaction chamber. So the lower it is, the more head presure it will have to deal with. Imagine trying to blow bubbles into a body of water at 6" of depth, and then at 3' of depth... the 3' would be much harder, no?
The tube diameter that the beckett's output must travel determines the pressure as well. If you go too small, you can create a back pressure on the injector itself, and you lose air intake, but if you go too small, the mixture can hang travel too slow in the pipe on its way down, and smaller bubbles can end up combining, and larger bubbles can end up rising inside the chamber... creating pockets of air that disript the throughput until the back-pressure on the injector causes it to lose its air intake. See, according to Newton's conservation of energy laws, as the pipe diameter decreases, the speed increases. As the speed increases, the pressure also drops.... this is the fundamental law that gives us bernoulli equasions and explains how venturis work. Anyways, the smaller pipe keeps the water flowing faster, and prevents it from regaining pressure until its inside the skimmer. If the pipes are too big, pressure increases, and we all know what happens to air bubbles when pressure increases (and its in a mix with something more dense like water)... it wants to rise with more and more bouyant force.
So the final response to your question is 'depends'... as Zephrant pointed out, there are no linear interpolations to be understood here... every variable is on a curve, and every ideal is relative. There are 'sweet-spots' for every design depending on the other design parameters.