With Global Secondary Copy, as you may already be aware it is just combining all the Backup from different Storage Policy Copy, into a single stream (single Tape Drive) when writing to a Tape Library
The benefit is cost saving on Tapes, as we will continue to write to the tape until it is full before we move on to the next Tape. Whereas if you do Aux Copy to Tape at a Storage Policy level, we will only Aux Copy the associated jobs for the specific Storage Policy.
A possible downside of using Global Secondary Copy is the restore speed. When using Global Secondary Copy we are leveraging multiplexing so we can write multiple streams to a single tape. However because Tape Medium is a sequential Media, during restore it might be seeking back and forth on the Tape Media to identify the required Archive File, resulting in slow read speed
Additionally a Tape will not be marked as Aged, unless all the Jobs on the Tape (across all 5 Storage Policy) has met retention.