What does the freenas say, is it also in 100 Mbps? if you have an ssh into it, you ran run this command:
[root@YourLinuxBox]# dmesg | grep -i duplex
e1000: eth0 NIC Link is Up 1000 Mbps Full Duplex, Flow Control: None
If your Bro's PC is gig, the only difference between you and him is that Asus DSL-AC68U and the 2 wires... so my first preference would be to plug in straight to the BT HH and see if you're getting Gig, if you can bypass the ASUS DSL-AC68U or swap the gigabit switch for the Asus does that change things?
Some switches have auto-negotiation, but if it's not, you can use a crossover cable to be sure. The other thing is that your ASUS DSL-AC68U may have a "WAN" port, which may only be 10/100 that you're plugged into.
Since you're plugged in directly to the ASUS, then your "link" is 10/100, but that's all it tells you, it doesn't tell you past the first switch (Asus DSL) whether it's 10/100 after that. So it's probably just your link, so try to narrow down where it says 10/100 and where it says gigabit. If you have a laptop, it would be extremely useful here to find out what links say gig vs. 10/100. Remove variables until you find the "bad" link.