Automatic off-line design is an attractive approach to implementing robot swarms. In this approach, a designer specifies a mission for the swarm, and an optimization process generates suitable control software for the individual robots through computer-based simulations. Most relevant literature has focused on effectively transferring control software from simulation to physical robots. For the first time, we investigate (i) whether control software generated via automatic design is transferable across robot platforms and (ii) whether the design methods that generate such control software are themselves transferable. We experiment with two ground mobile platforms with equivalent capabilities. Our measure of transferability is based on the performance drop observed when control software and/or design methods are ported from one platform to another. Results indicate that while the control software generated via automatic design is transferable in some cases, better performance can be achieved when a transferable method is directly applied to the new platform.