To start, Arma 3 multiplayer performance is terrible for everyone, not just you. It's due to the way they have it setup, where client FPS is limited by the server's FPS. So, everyone gets terrible performance in multiplayer. It's not just those with AMD hardware or just you, it's all of us, even those with Intel/Nvidia setups. It's very rare to see 60fps in MP, without it being a small group on a powerful server. The average performance is around 30fps.
Second, AMD CPUs have a history of being worse for gaming, with Arma being one of the worst. This is because of the architecture of the AMD CPUs. They are built for multicore, lots of little, weaker cores. Intel CPUs are built with fewer, but more powerful cores. Gaming in general currently uses fewer cores, often placing the load on 1-2 cores primarily. Because of this, Intel CPUs get better performance. Arma places an extra heavy load on the first core, with very little distributed to the rest, more so than most other games. Because AMD's cores are weaker, when it's only using a few cores, it gets less performance.
So basically, you're screwed, but so is everyone else. There are some tweaks you can use, for example I believe that one of the most common recommendations is to set your graphics settings as high as you can, to offload work from the CPU to the GPU.
From the sidebar:
http://steamcommunity.com/sharedfiles/filedetails/?id=385577681
http://wiki.day0.com.au/ArmA_3_Performance_Tweaks_and_Settings_Guide
http://segmentnext.com/2013/09/16/arma-3-tweaks-guide-graphics-and-performance/
"WARNING: In Multiplayer, FPS often depends on the performance of the mission loaded onto the server and the performance of the server itself. If you find yourself getting high FPS on one server but low FPS on another, you might want to consider switching servers or asking for a better-optimized mission to be put on the server. Some optimized missions I know of included BeCTI Warfare, Antistasi Altis, PANDORA: the Insurgency, and others. Try them out and see how you like them!"