Try these settings:
See if the issue persists.
Also, it is possible that this is a side effect from not having Transparency AntiAliasing enabled. This mesh seems visually as something that would be rendered using alpha-testing (transparencies), and if you use default Multisampling with no TSAA (Analytical or Supersampling), then this might be the cause. Unfortunately, if that's a DX9 game, you're fubar, since AMD cannot into transparency AA on DirectX 9 as of yet. In fact, it can't even override DX9 app's AA settings.
But judging from the fonts in the right corner of the screenshot, I assume it's Fallout 4, in that case it's using temporal antialiasing. Then the problem might really be the Radeon Sharpening from the driver settings. Or maybe you used FXAA from control panel when you had the 1060, and that smoothed out the pixels on the mesh. There are also other probabilities I can think of, but those are the most likely ones.