Even the highest FSR setting "Ultra Quality" has some visible loss in image quality. Sharp high-contrast edges particularly are effected, like on the harbor building. On the other hand, water surfaces look indistinguishable, even at faster FSR modes.
In Anno 1800, I'd say a good compromise between quality and FPS is FSR Ultra Quality, which still gains a lot of performance.
We see a bunch of surprising results here. For example, the RX 6800 XT sees negative performance scaling for the lower-quality FSR modes. I suspect this is because the game becomes CPU limited at around 100 FPS. We also see negative scaling with the GeForce RTX 3080 Ti, which seems to be a bug in the FSR implementation—at 1440p, the game runs at around 90 FPS no matter the FSR mode.
In 4K, the CPU bottleneck that we saw on the RX 6800 XT disappears because at that resolution, no card can exceed 100 FPS significantly, not even with FSR Performance. The GeForce RTX 3080 scales correctly with FSR now, reaching performance levels very similar to the RX 6800 XT.