SSIS v/s Replication v/s logshipping
As always, it depends on a lot of factors, but I'll answer like this:

If the SSIS package takes only the deltas from the last run and performs well, I'd keep using the SSIS, since its something that is already working and I assume you are familiar with. 

Log shipping and replication will work, but they have drawbacks. For instance, with log shipping you will have to disconnect all of your users when restoring the log backups on the target server.