Ok, I give up.
I gave a shot to OpenWRT AA (so linux 3.3.8), and FYI, I had to include additionnal firmware (rtl8168e-3.fw), that I didn't needed before owning this RTL chip. It is related to these 8111EVL as they are seen as RTL8168evl/8111evl whereas older NICs are seen as 8169/8110. I don't know if it is required for some offloading, or if it is a "fix" to harware issues.
Used the exact same commands without reproducing the issue.
Btw, linux driver seems to have had problem with this chip before being fixed: https://bugzilla.kernel.org/show_bug.cgi?id=14962
I'm definitly thinking about bsd re driver having an issue with this chip (more likely the other way around, but you get the idea :)).