I'll make the assumption that you are moving large amounts of data. The typical solution to this problem is to break the copy up in to smaller number of rows. This keeps the hit on transaction log smaller. I think this will be the preferred answer.
The other answer that I have seen is using Bulk Copy, which writes the data out to a text file and imports it into your target db using Bulk Copy. I've seen a lot of posts that recommend this. I haven't tried it.
If the schema of the target tables isn't changing could you not just truncate the data in the target tables instead of dropping and recreating?