A Hopf bifurcation with translational invariance has been widely considered as an appropriate model for the appearance of spiral vortices in counter-rotating Taylor-Couette flow. Our experimental work demonstrates that flow conditions close to the axial boundaries are responsible for the type of bifurcation scenario, i.e., either asymmetric pure traveling waves or more complex behavior, such as defect states or symmetric mixed states appearing from a Hopf bifurcation. The measurements were performed in the first Taylor-Couette experiment with independently rotating endwalls confining the system in axial direction. The rotation rate of the (synchronous) endwalls is found to be an essential control parameter for the spatial amplitude distribution of the traveling waves and also reflects symmetry of the corresponding flow pattern appearing from the Hopf bifurcation.