Performance of a Trigger vs Stored Procedure in MySQL
For the sake of simplicity, triggers are the way to go for implementing any kind of tracking of database changes. However, you need to be aware of what happens under the hood when you use triggers.

According to MySQL Stored Procedure Programming, page 256 under the head "Trigger Overhead" says the following:


  It is important to remember that, by necessity, triggers add overhead
  to the DML statement to which they apply. the actual amount of overhead
  will depend upon the nature of the trigger, but --- as all MySQL
  triggers execute FOR EACH ROW --- the overhead can rapidly accumulate
  for statements that process large numbers of rows. You should
  therefore avoid placing any expensive SQL statements or procedural
  code in triggers.


An expanded explanation of trigger overhead is given on pages 529-531. The conclulding point from that section states the following:


  The lesson here is this: since the trigger code will execute once
  for every row affected by a DML statement, the trigger can easily
  become the most significant factor in DML performance. Code inside the
  trigger body needs to be as lightweight as possible and -- in
  particular -- any SQL statements in the trigger should be supported by
  indexes whenever possible.


Not mentioned in the book is another factor when using triggers: When it comes to audit logging, please be aware of what you log data into. I say this because should you choose to log to a MyISAM table, each INSERT into a MyISAM table produces a full table lock during the INSERT. This can become a serious bottleneck in a high-traffic, high-transaction environment. Additionally, if the trigger is against an InnoDB table and you log changes in MyISAM from within the trigger, this will secretly disabled ACID compliance (i.e., reduce block transactions to autocommit behavior), which is cannot be rolled back.

When using triggers on InnoDB tables and logging changes


The table you log to is also InnoDB
You have autocommit turned off
You setup START TRANSACTION...COMMIT/ROLLBACK blocks thoroughly


In this way, audit logs can benefit from COMMIT/ROLLBACK as would main tables.

Concerning using stored procedures, you would have to painstakingly call the stored procedure at every point of DML against the table being tracked. One could easily miss logging changes in the face of tens of thousands of lines of application code. Placing such code in a trigger eliminates finding all those DML statements.

CAVEAT

Depending on how complex the trigger is, it can still be a bottleneck. If you want to reduce bottlenecks in audit logging, there is something you can do. However, it will require a little infrastructure change.

Using commodity hardware, create two more DB Servers


Distribution master (DM) to relay audit info only
MySQL Server for Auditing (AU)


This will server to reduce write I/O on the main database (MD) due to audit logging. Here is how you can accomplish it:

Step 01) Turn on binary logging in the main database.

Step 02) Using an inexpensive server, setup MySQL (same version as MD) with binary logging enabled. This will be DM. Setup replication from MD to DM.

Step 03) Using a second inexpensive server, setup MySQL (same version as MD) with binary logging disabled. Setup each audit table to use --replicate-do-table. This will be AU. Setup replication from DM to AU.

Step 04) mysqldump the table structures from MD and load it into DM and AU.

Step 05) Convert all audit tables in MD to use the BLACKHOLE storage engine

Step 06) Convert all tables in DM and AU to use the BLACKHOLE storage engine

Step 07) Convert all audit tables in AU to use the MyISAM storage engine

When done


DM will replicate from MD and record stuff in its binary log only
With --replicate-do-table filter on all audit tables, AU will replicate from DM


What this does is store audit info on a separate DB server and also reduce any write I/O degradation that MD would normally have.