check for duplicate entry vs use PDO errorInfo result

INSERT + check status should be a better approach. With SELECT + INSERT you can have another thread insert the same value between the SELECT and the INSERT, which means you would need to also wrap those two statements in a table lock.

It is easy to err on the side of too much defense in your coding. Python has the saying that "it is easier to ask for forgiveness than to ask for permission", and this philosophy is not really Python-specific.

You could be executing this with a try catch block:

try {
   $prep->execute($values);
   // do other things if successfully inserted
} catch (PDOException $e) {
   if ($e->errorInfo[1] == 1062) {
      // duplicate entry, do something else
   } else {
      // an error other than duplicate entry occurred
   }
}

You could also look into alternatives such as "INSERT IGNORE", and "INSERT... ON DUPLICATE KEY UPDATE" - though I think those are MySQL specific and would go against the portability of using PDO, if that's something you're concerned about.

Edit: To more formally answer your question, to me, solution #1 (the defensive programmer) in full usage effectively eliminates the point of the unique constraint in the first place. So I would agree with your thought of letting MySQL take care of data checking.