Dithering adds texture and makes surfaces look rough. It's fine when applied to a rock or patch of dirt, but it's an amateur mistake to use it everywhere.
Anti-aliasing is used a fair bit in pixel art, but less so in artwork designed to look 8-bit. There weren't enough colors and palette space to anti-alias in older games, so it looks out of place when replicating the look.
When used correctly, dithering can be a work of art itself. Pretty much all the artists I know who work on actual 8-bit platforms use both dithering and AA extensively, hardware permitting.
Anti-aliasing is used a fair bit in pixel art, but less so in artwork designed to look 8-bit. There weren't enough colors and palette space to anti-alias in older games, so it looks out of place when replicating the look.