Flow in a cylinder driven by the co-rotation of the top and bottom endwalls displays distinct instability mechanisms, depending on whether its aspect ratio (length to diameter) is large or small. When the cylinder length is about the same as its diameter, the two mechanisms compete and lead to a stable mixed mode solution. Using numerical computations of the three-dimensional Navier–Stokes equations, together with equivariant bifurcation and normal form theory, we explore the nature of this mode competition, both from a flow physics point of view and from a dynamical systems with symmetry point of view. The results help to clarify the distinct behaviours observed experimentally in some short and long cylinder flows.