For most people in most years, it doesn't matter much.
The major factors to consider are: (1) wind, (2) weather, (3) daylight, (4) the sun, (5) history, (6) air travel, (7) what you want.
(1) Many will tell you differently, but based on recorded historical data, surface wind is too variable in most places to favor one direction over the other. There are a few notable exceptions, such as Wyoming and the Pacific Coast, but you don't want to plan your trip around the exceptions.
(2) Typically, when looking for good weather, westbound cross-country travelers can start earlier than eastbound cross-country travelers. So to some extent it depends on when you want to start.
(3) If you're going cross-country, neither direction favors more daylight. But if you're going north-south, then one direction may give you more total daylight than the other direction.
(4) You don't want the sun in your eyes, nor in the eyes of the drivers behind you. If you like to start at the crack of dawn, then you probably want to go west. If you like to start late and ride into the sunset, you may want to go east. If you start late and quit early, it won't matter.
(5) Many people like to retrace the route of westward expansion, which suggests westbound.
(6) If you are riding to or from your house, or getting to one end via automobile, then it's usually easier if you can fly to the start and ride home rather than the other way around. It's just easier to pack your bike at home when you have plenty of time.
(7) None of these factors are overwhelming, so if you just have a hankering to go one way or the other, then go that way.