The COPY command is executed fully on server side - input/output is related to server side streams. But these streams can be redirected to client side - when you run COPY in a pre-configured environment. \COPY is this case.
\COPY is psql's commands - it can be executed only from psql and it prepares internal environment for a possible read/write from client side streams, and it execute COPY commands.
So difference between COPY and \COPY is minimal. \COPY is COPY executed in different configuration for a possible read/write data from client. The performance should be same - \COPY can be a little bit slower due to network overhead (it is clear), but it should not be significant. In this case the communication protocol should be effective.