SSL cert in the F5 and in the respective web server

One of the biggest adavantages is the simplification of the certificates management. Among the others advantages already told previously, you may centralize the management of your SSL certificates by placing them at the same location, ie on your Big-IP. Even then, if you have a wildcard certificate, then you could create a profile at the Common level and use it for any Client SSL profile that would need it, instead of recreating a specific SSL profile for each VS.

The Big-IP will be a client to the backend server, and does not deal with interactive warnings you would get in a browser, so you can easily deploy a self-signed cert on your backend server and not really care about it. Of course, it depends on the level of your security standards in your organization.