Select into is much much faster in terms of performance as it can run in minimally logged mode. For this, you need to have the database in Bulk-Logged recovery. When you use Bulk-Logged recovery, and when you execute a Select into command, it is considered a bulk operation. But you would lose the option of doing a point in time recovery while using the log backup that has a bulk operation in it.
Another difference you may already be aware of is that select into creates the destination table but does not have any constraints created similar to base table. Incase of Insert followed by a select, your destination table needs to be created ahead of time.