CommServe DR is a “basic” backup of your CommServe Database scheduled on a daily basis and with its own storage policy. This option offers the ability to restore your CommServe however it can take an extended period of time.  No replication here. Refer: https://documentation.commvault.com/commvault/v11_sp20/article?p=43516_1.htm

CommServe LiveSync (HA) - you configure a secondary instance, where replication of its database happens every xx mins/hours depending on your environment and in case of a disaster at your PROD site where your Master CommServe is located you can switch to the Secondary CommServe pretty quick.  Refer https://documentation.commvault.com/commvault/v11_sp20/article?p=102841.htm

It comes back to the criticality of your environment, RTO etc.

Another way to look at it:

CS DR is basic and requires less work up front, but more work when there’s a disaster.

Livesync is a more automated response recovery method.  Requires more work up front, but a big time savings when an actual disaster hits!