You might want to web-search for "FreeBSD
Capsicum".
In other words, to elaborate somewhat on
SirDice's post: AppArmor is a (more correctly, one of diverse) Linux approaches to (kernel related) security (others being Tomoyo, SELinux, ...). Obviously FreeBSD is concerned about the underlying problems, too, and obviously FreeBSD has been/is working on a proper solution, too.
One needs to understand that those "security solutions" address what are in fact quite diverse issues like stack protection, proper memory segment usage, etc.
The problem class you seem to be interested in is typically addressed by capability management, i.e. by some kind of (software) system that associates a set of necessary capabilities (like access to certain devices, ports, etc.) with a given application that is then checked and enforced by the kernel.
Capability management has been researched quite long and well and has shown to offer excellent potential. Unfortunately the number of readily supported applications/daemons is still quite small but you may, of course, add more. Just look up
capsicum(4).
Note, though, that FreeBSD (if properly set up) is quite safe out of the box and capsicum (from today's perspective) is considered something more in the high-security realm. For practical purposes the combination FreeBSD and Hiawatha already offer a rather solid level of security. My advice is therefore to rather concentrate on a "watertight" standard FreeBSD and server(s) setup and configuration.