Fortunately, the best security approaches (HW-centric) are portable to both w/ FreeBSD getting most prototypes. You can already run capability-secure FreeBSD via Cambridge CHERI project. Criswell's people are doing lots of stuff with FreeBSD and maybe Linux:
https://www.cl.cam.ac.uk/research/security/ctsrd/cheri/
http://sva.cs.illinois.edu/pubs.html
Examples for Linux include these:
http://scholar.lib.vt.edu/theses/available/etd-10112006-2048...
https://web.archive.org/web/20120509155852/http://archives.e...
https://docs.google.com/file/d/0B1i_Zf52vJctMTA4YTI1MmUtNzdj...
That doesn't even include software-related techniques like microkernels, low TCB software, safe low-level languages, and automatic compiler transformations for security that neither are adopting. They're both low-medium assurance by my standards due to cultural refusal to apply what's proven to work. So, I already have predictions about tech-transfer of papers above to Linux/FreeBSD use at large. You can probably guess how optimistic I am. ;)