Dithering was set to Shiau-Fan Slight banding in the lighter areas of the background, and the building and lips are again missing colours from the original. Next, let's try Color Quantizer with standard settings, a two factor gradient priority, and 256 colours. At the expense of smaller areas with unique colours. Overall, though, the final result is much less grainy looking than Photoshop's effort. Notice how the gradients are quite nicely retained, although here and there some issues pop up (lips/makeup, building, arm highlight, and greenery are missing colour). RIOT features a newer 'NeuQuant neural-net' colour quantization algorithm. Next up: RIOT (Radical Image Optimization Tool).

Obvious banding issues, and a very grainy result. The best visual quality I could achieve in SfW (diffusion dither at 81%, perceptual). Here is the original version zoom (32101 colours): For a good conversion you will have to look elsewhere. Second, Photoshop's Save for Web colour reduction algorithms are quite old-fashioned, and (far) better methods are available. Second, the quality of the GIFs you produced in Save for Web (SfW) prior to the purchase of the new laptop were never any 'better' - it merely means that the previous screen was unable to display the results at a decent enough quality to actually discern the differences between the original and the GIF version with reduced colours. First, JJMack is correct: lots of colours (around 32100) in this example do make it harder to convert without grain.

Make animated gif in photoshop