Here's a document describing the best practices around connection and persistence mirroring:
https://support.f5.com/kb/en-us/solutions/public/7000/200/sol7222.htmlbestpractice
Persistence will keep users going back to the same pool member. If you have a fail-over and aren't mirroring persistence, the user could get send to any server in your pool.
Connection mirroring copies actual state data and can add much more overhead. If there was a fail-over in the middle of an HTTP request, the user might see a few objects fail to load but could easily refresh the page. Due to the overhead involved and given how forgiving HTTP is, mirroring connection data for it isn't recommended.
If you're using persistence, I'm assuming your application requires it so you should definitely mirror your persistence table to the other unit.