AES-NI is broken on FreeBSD for things that need cryptodev support.
If you do not load the AES-NI kernel module, OpenVPN will use OpenSSL's internal AES-NI code which is quite fast.
I have had reports from a customer that they were able to push a sustained >600Mbit/s transfer over OpenVPN on hardware with AES-NI.
AES-NI is not broken on FreeBSD. It's just that the modes which are implemented (in cryptodev) can't be effectively pipelined, and as a result, AES-NI is … hobbled on FreeBSD.
However, the problem is now understood, and we're fixing it. You should be able to get 750-850 Mbps with the right hardware using IPSEC tunnel mode. (In theory, AES-NI is good for 2Gbps per core, but using tunnel mode adds a few bytes to the packet, the encapsulation/decapsulation costs a few instructions, and that test was using a single core processor and 1Gbps Ethernet interfaces.)
With the right hardware ($$$), you should be able to run 20-50Gbps throughputs. 8) No, I did not stutter.