Our SOPs: CP (LHS) calls and actions RTO whether PF or PM. FO (RHS) when PM calls the failure and then monitors the RTO, or when PF keeps the ac straight until CP takes control for the RTO. If the LHS is CP under trg, the same applies, though as LTC in the RHS I retain the right to call/action the RTO.
It's a good question of cockpit philosophy, though. We trust the FO to call 'Engine failure' etc and would respond with RTO, so why not allow him to call 'STOP'? We expect the FO to call the failure and then carry out the RTO if my ageing heart gives out at a critical moment, why not trust her with the full deal all the time? It would make transition to command smoother. In a previous (military) life, either pilot (and indeed the engineer I thnk) could call the RTO and whoever was PF would action it.
My 2 pennyworth - hope it helps
DH