Feedback flashing ratchets are thermal rectifiers that use information on the state of the system to operate the switching on and off of a periodic potential. They can induce directed transport even with symmetric potentials thanks to the asymmetry of the feedback protocol. We investigate here the dynamics of a feedback flashing ratchet when the asymmetry of the ratchet potential and of the feedback protocol favor transport in opposite directions. The introduction of a time delay in the control strategy allows one to nontrivially tune the relative relevance of the competing asymmetries leading to an interesting dynamics. We show that the competition between the asymmetries leads to a current reversal for large delays. For small ensembles of particles current reversal appears as the consequence of the emergence of an open-loop like dynamical regime, while for large ensembles of particles it can be understood as a consequence of the stabilization of quasiperiodic solutions. We also comment on the experimental feasibility of these feedback ratchets and their potential applications.