The function of the reactor's control rods is to regulate the amount of fission occurring in the fuel. They are made of Boron and Cadmium and other elements, to absorb most of the neutrons. So the higher portion of them inserted into the fuel, the more absorption and the less fission reactions occur. And removing them has the opposite effect, allowing more neutrons to scatter around, thermalize, and cause fission.
So the principle has nothing to do with their shape or from which side they are introduced. You could have control layers in a sandwich-like reactor, which go in and out to control fission rate in a similar way.
However, the specific way in which they are built, geometry and shape, might be important for mechanical and engineering reasons. If a layer needs to be very thin, mechanically would be undesirable because of its deformability at high temperatures, which could lead to accident scenarios more likely.
Summing up, the direction and shape of the controls is not directly related to the concept of the reactor, but rather to the feasibility and engineering constraints.