>>42224183Yes, Mirror Move keeps a list of the last moves that were targeted at the user by the Pokemon that are still on the field. If the user has not been targeted (with a callable move) by a Pokemon that is still on the field, it fails to execute. So it is generally far more likely to fail than Copycat, and it's more likely to fail in singles than in doubles, and it cannot copy moves that target the user, unlike Copycat.
The one thing Mirror Move can do that Copycat cannot do, is call moves from several turns ago, if it has not been targeted since then, but the Pokemon that last targeted it is still on the field.
Copycat is far more flexible, can copy moves that were used when the Copycat user wasn't even on the field yet, moves used by Pokemon that aren't on the field anymore, moves that target the user, and even moves that were used by the Copycat user on the previous turn.