F5 Viprion 2400 acting as a reverse proxy

It's interesting that you point out IIS as a reverse proxy. Traditionally speaking, IIS has never really (natively) had the ability to be a reverse proxy with URL rewrites until 7.5, while Apache has had this functionality since the dawn of time. In any case, it is safe to say that an F5 BIG-IP, regardless of physical platform, is designed to be a reverse proxy. Above and beyond anything else it can do, reverse proxy is a core function. BIG-IP can also do forward (web) proxy, though that isn't a native thing.

As for the URL rewrite stuff, there are a few options. In 11.4, there's a new rewrite profile that provides, among many other things, URL translation. Prior to that, and depending on the complexity of your environment, you can either build it yourself with some relatively straight forward iRules, or use a pre-built iRule called "ProxyPass" - appropriately named to suggest capabilities similar to Apache's ProxyPass.