I'd say it's a close tie between Mirroring and Log Shipping.
If you wanted a fully HA Mirror solution then you would also need a witness server and an application that is modified to use the latest connectors allowing you to provide both the Primary and Failover servers. So that would mean maintaining to some extent 3 database servers, and assuming that you have applications using the latest and greatest db connection methods. But the failover would be automatic. So more work on the front end and more watching on daily maintenance for logs and 3 servers, but backend (ie. failover) should be transparent.
Log Shipping has less work on the front end, little daily watching on maintenance, but a bit more work on the back end (ie. needing to use failover).
So in the wash which one would take more Administrative effort?