Forwarding L2 & Forwarding IP virtual servers - when to use them?

L2 is L2, so it is useful when you have the big-ip in L2 mode, so inline between two switches which force the traffic on L2 level through the box.

forwarding IP would be useful for pool members behind the big-ip as default to get external access. you configure a forwarding IP server on the pool member VLAN and have a default route towards the internet. servers send there requests towards the big-ip where the forwarding IP virtual server picks it up looks at the routing table and sends it forward there.

you need to setup your routing on the big-ip as you would on a router, the forwarding IP virtual server follows the routing table it doesn't create new routes or such.