BIG-IP - Layer 4 or Layer 7 LB

It is both and more. You can use it as L4 (per packet, half proxy) by applying a FastL4 profile to a Performance Layer 4 Virtual Server or L7 with a Standard Virtual Server with a HTTP, XML or some other L7 profile. You could also use an F5 as a L3 router and for forwarding at L2.