I had a question from a customer who wanted to keep MQ archive logs for a year (for audit and problem determination purposes).
Should they use MQ log compression (SET LOG COMPLOG or CSQ6LOGP COMPLOG)?
The short answer is - let HSM compress it when the data set is migrated.
The log compression function was implemented when disks were much slower, and active logs were unable to keep up with the required throughput. These days DASD is much faster.
If your archive logs are migrated then HSM can compress them better than MQ can. The migrated archive are smaller than the original data sets. You can use the HSM LIST DSN(...) command to show the original space, and the current space used.