Fallout 4 Benchmark Results: Higher Resolutions And Bottom Line shows the Fury averaging 59fps at that resolution, so it's not an AMD problem.
Also: Fallout 4 Performance Impacted By Latest Windows 10 Update, Fix Discovered it's a few months old, but you could try the fixes.
Well, it does not run at 50+ FPS with the latest game+driver. Not sure what's causing it but it seems like an issue with GPU usage.
EDIT: Looks like an issue with Freesync + the game's forced vsync.
Edit2: changing bForceIgnoreSmoothness to 1 and iPresentInterval to 0 solved the issue. 45+ FPS in game freesync seems enabled but I can see tearing.