Is Log Shipping or Mirroring a better solution for Disaster Recovery? I am planning an index rebuild, however my logs are prone to huge overblown sizes.

In fact I was leaning towards doing an intelligent re-indexing, but since the fragmentation levels are greater than 30% I thought I should do a rebuild.

My databases use the full recovery model.  Should I change the recovery model to Bulk logged before I do the rebuild later this weekend when there are less transactions happening.

Log shipping is enabled as a DR solution in these databases.

What do you suggest if my latency is quite high? Is there a better DR solution that I should look into?
I think this is kind of the same question as the other one you just posted. there are a couple of new points you address:

Bulk logged mode doesn't make the logs shipped over the wire smaller. It just makes writing to the local log file less IO intensive. Once the log has to be backupped, alle changed pages haved to be included in the backup. The end result is that your trans log backup will be just as big.

If you already have High latency, changing to mirroring will not change that. the only way to spread the load is: stop doing rebuild and change to a spread reorganize strategy (as I mentioned in your other question.)

Or as somebody else there mentioned, start doing more frequent log backups and ship smaller log backups in a higher frequency.

Just based on what you are telling us now. (the high latency) I personally would not advise to change to mirroring. But the choice between mirroring and log shipping should be based on many more items then only latency.