TL;DR: it’s complicated.
Assuming the wind doesn’t blow, there’s no difference. You’re flying X miles either way.
However, the wind does blow, and IIRC it tends to blow from west to east near the poles and east to west near the equator. Since planes fly in air, flying *with* the wind moves you over the ground faster, while flying *into* the wind slows you down (relative to the ground). So flying from the UK, it’s easier to fly westward than to fly eastwards, until you hit the equatorial region where it gets harder. But once you’ve crossed over well south of the equator, it will get easier again.
This is ignoring that most planes fly great-circle routes, which often route “unpredictably” (to common intuition) on a map, because the Earth is a sphere and not a 2D grid.
Earth rotates at about 1,000 miles per hour at the equator, but they don’t experience 1,000 mile per hour winds because most of the air moves with the Earth. Therefore, Earth’s rotation isn’t a significant factor aside from how it drives wind currents.
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