MYSQL Read Replica Bottle Neck
If replication is using Row Based Replication (RBR), then, say, an UPDATE statement is faster on the Slave than on the Master.  This is because all that is sent to the Slave is the changed record.  The Slave does not have to think, does not have to search for the row, does not get the rows that don't need to change.

With Statement Based Replication, the Slave is essentially repeating whatever complex processing was done on the Master -- with an exception:  If there are a bunch of SELECTs happening to figure out what to UPDATE/INSERT/DELETE, then those happen only on the Master.

If any server has "high" CPU usage, crank up the slow log; let's see what is causing it.  Almost always, performance can be improved by a better index, a reformulation of a SELECT, etc.