We report on the experimental investigation of the large-scale instantaneous flow structures in turbulent Taylor-Couette flow using tomographic particle image velocimetry. The results indicate three distinct regimes for counter-rotating flow within a shear Reynolds number range of 11 000 < Re _S < 47 000. Close to only inner cylinder rotation, large-scale structures are aligned in the azimuthal direction, similar to Taylor vortices. Near the point of only outer cylinder rotation, we observe columnar vortical structures in the axial direction, which are associated with small Rossby numbers. This is the first time such columnar structures are reported in a fully turbulent Taylor-Couette flow. A transition between these two regimes is observed around the point of exact counter-rotation, where the instantaneous azimuthal structures are inclined with respect to the walls. Furthermore, it is shown that the reported transitions in the turbulent flow structure modify the angular momentum transport, thereby affecting the torque scaling.