Rsync essentially moves the bits from one place to another, its a network copy of the data. The data is not processed or interpreted, just shuttled through the network and written to disk.
MongoDB's replication mechanism inserts and validates the data, creates and updates indexes, and applies the operations that have occurred since the sync started to catch up. It's doing a lot more work.
You can think of it like getting the notes for a class you missed from friend. You could go to the xerox machine and produce a copy or you can open a fresh pad of paper and start transcribing (reading and understanding what he wrote, and writing down your own copy in your own handwriting).