Log implications of copying data from one table to another
Even with Simple Recovery Model, you still have to log every part of the insert in case it fails and you need to rollback. If you are moving all of the rows (or almost all of them) as a one off process you may be better off just renaming the table and then altering the columns to be what you need.

If this is a process that runs over and over again (E.g. an end of month process) then you might want to look at partition switching.

If neither of those work, then you'll probably be better off batching your inserts. Michael Swart has a good blog on how to do that. See also Take Care When Scripting Batches.