Proper size of cezve matters. Normally, it is ideal to fill up the cezve up to one third to the half of its height before beginning the brewing process. You need the rest of the height during the foaming time. You cannot fill it up to the neck and start brewing. In that case, at the end, when bubbles start to appear, it will spill over.
In Turkey, cezve is usually sold in sets. You can see a set of old style tin-plated copper set of five cezves in the image below. This set includes 1-cup to 5-cup cezves. However, I don't recommend them as the metal is not thick, so the heat is not homogeneously distributed while brewing. A second disadvantage is, tin plating could be worn away in time and copper oxidizes easily. The green colored copper-oxide is quite poisonous.
A modern stainless steel cezve set is also shown below. (Image is copied from Hisar cutlery firm's website.) This set includes 2-cup to 4-cup cezves.
As you can see, both sets include different sized cezves for different servings.
(A distinct advantage of possessing more than one cezve at home has another advantage: You may prepare Turkish coffee with or without sugar at the same time in two different cezves in case your guest wants to consume a different recipe than yours.)
So, I assume I make my point that the size matters and also the count is important. Let's talk about the shape.
Be practical, see inside. Check the spoon for stirring in the second image. You can see its length is ideal for stirring without burning your hand. Your hand will be over the vaporizing coffee most of the time. Find your ideal spoon, together with your cezve.
As it can clearly be seen, the shape is more or less the same. Wider bottom is mostly a result of finding proper balance on top of the stoves for small sized ones. You can see it when you look at them in the sets next to each other. If the bottom is wider, the neck seems narrower. When you have heavier stainless steel cezves, balance is already there, so the bottom is not that wider, thus the neck is not that narrower.
Still, I must admit that, a narrow neck is also related with the foam. The foam is formed by carbon dioxide packed in coffee lipids. When you heat the coffee, the carbon dioxide is extracted together with lipids and cannot be solved after some threshold in water. Those carbon dioxide changes its phase to gas form such as any effervescent, forming bubbles. This is the foam of Turkish coffee. If you try to brew Turkish coffee in a pan, the bubbles will be too far away and cannot survive in the surface of the coffee. They will soon pop and fade away. If they are close together, some irregularities of coffee (such as small particles in the coffee powder) stick on the surface of the bubbles and keep them together. Then, the bubbles form the foam. That's the reason a narrow neck helps to keep the foam.