Authoritative Server vs Relayed Server Efficiency

How similar is the efficiency between the 2 in terms of CPU usage and network load for a 1v1 game?
The authoritative server would relay messages as soon as it gets them without checks on the content with a tick rate of 60. The clients would send 60 messages per second.

Hello @Raanaya

If an authoritative match is simply relaying messages then the performance difference to a relayed match should be negligible.