Will it be less performant than doing the same thing in a stored proc. Probably not but with all performance questions the only way to really know is to test both approaches with a realistic data set (if you have a 2,000,000 record table don't test with a table with 100 records!)
That said, the choice between a trigger and another method depends entirely on the need for the action in question to happen no matter how the data is updated, deleted, or inserted. If this is a business rule that must always happen no matter what, a trigger is the best place for it or you will eventually have data integrity problems. Data in databases is frequently changed from sources other than the GUI.
When writing a trigger though there are several things you should be aware of. First, the trigger fires once for each batch, so whether you inserted one record or 100,000 records the trigger only fires once. You cannot assume ever that only one record will be affected. Nor can you assume that it will always only be a small record set. This is why it is critical to write all triggers as if you are going to insert, update or delete a million rows. That means set-based logic and no cursors or while loops if at all possible. Do not take a stored proc written to handle one record and call it in a cursor in a trigger.
Also do not send emails from a cursor, you do not want to stop all inserts, updates, or deletes if the email server is down.