Not sure you would want to compare those two technologies since Mirroring will no longer be available in future versions of SQL Server. For those reasons, it's recommended not to use Mirroring on new development.
Log shipping is more of a DR solution. Mirroring can be more HA if using synchronous/automatic failover. But both have different things they address and both have different considerations. There are other options available for HADR depending on your environment, needs. 
This article is a little bit old but is still a pretty good reference on options, considerations, benefits, etc:
An overview of High Availability and Disaster Recovery solutions available for SQL Server

Sue