Your card is only marginally slower than mine, so you should be CPU-limited (as I am), not GPU-limited.
Check your video card usage (using any kind of hardware monitoring or overclocking tool). Does it reach 100% in the battle? I have fixed all known AMD compatibility issues, so unless there's some GLSL instruction I'm using that does not play nice with AMD cards (which should not be the case; on the AMD GLSL compiler I profiled the shaders on, the performance spec looked fine) I have no idea what could cause this if it is an issue with your type of card.
If you find that your card is not reaching 75-100%, then that means one of two things: either your card is limiting its output and slowing the game down that way, or somehow the change of card caused bugs/problems that result in a much higher CPU load. If that's the case, it's up to you to fix that on your end.
If your card is reaching 75-100% load, then I need you to try different settings via settings.json and see if that improves things. Use a consistent mission like The Last Hurrah to gauge performance.