SQL Server 2008R2 - Replication - Log Files / Indexes
but wouldn't they therefore create the same level of fragmentation on each server? 


No. Fragmentation is physical, replication is logical. The same sequence of insert/delete/update may produce different physical indexes, but transnational replication may not even produce the same sequence of insert/deletes/updates. Even with non-filtered publications, the replication agent can fail, rollback and retry when applying the changes.


  surely if the log has recorded and performed the same actions due to the replication they would be similar


Not at all. The database activity may extend well beyond the area covered by replication (in other words, the database may contain more than just the subscription articles). But, more importantly, the log structure is shaped more by backup schedule and log retention than by activity. Read more here.