You have headwinds the whole way no matter which way you go. Murphy's law.
You can ignore most of the "prevailing winds" wisdom from friends. Most of it has no scientific basis. In my two trips across the country, once in each direction, I had about an equal amount of headwinds and tailwinds. The only reason I know this is because I took a wind meter and measured twice a day. If I only had my gut to go on, I'd swear that I had a lot more headwinds than tailwinds. Headwinds are more memorable.
There are a very few places, however, where the winds are somewhat predictable. I think Wyoming is one. The Pacific Coast in the summer is another. But in most places, the winds vary a lot, and even if there is a slight pattern, the bias is slight (even though it might not be slight the day you are there). Furthermore, the bias changes from season to season. It's pretty common to have a headwind one day, a tailwind the next, and a headwind the next.
On my most recent cross-country ride, I thoroughly studied the wind rose data that Pat cited before I went. But I found that the actual winds I encountered bore little resemblance to the wind roses. The problem is that an individual cyclist's experiences is too small of a data set to be statistically significant.
I agree with Pete that any consideration of wind should be a minor factor in deciding which way to go.