The two graphics card testing links below shows that Arma 3 currently perform poorly on AMD's latest RX 470 and RX 480 cards.

http://www.hardwareunboxed.com/rx-480-8gb-vs-gtx-1060-6gb-battle-of-the-mid-range-contenders/
http://www.hardwareunboxed.com/gtx-1060-3gb-vs-rx-470-4gb-best-value-at-200/

The performance on AMD's previous generation (R9 390, R9 390x) however, doesn't show this performance dip on Arma 3.

Reference: http://www.hardwareunboxed.com/amd-radeon-rx-480-benchmark-review-23-games-tested-three-resolutions/

I am currently getting around an average of around 30 FPS on a Tanoa Invade Annex server with no other players on. On either ultra or high settings, 1080p. My CPU is an i5 2500k oc to 3.7ghz on all cores along with an AMD RX 480. Radeon driver version 16.10.1 and Arma version 1.64.138732

I made a roughly half an hour capture of hardware monitoring while on the Tanoa Invade Annex server, in case it can be of any aid. http://i.imgur.com/UCQ7thA.png
I noticed that the GPU appears to be underutilized.