I completed the Southern Tier this year, leaving St. Augustine April 7th - just about your same time frame. I also read numerous accounts of west-east vs east-west and decided to go westward because of the stories I read of headwinds from El Paso to Del Rio (450 miles). Consequently, I had a tailwind through that section, but ended up fighting headwinds from about the New Mexico/Arizona border to San Diego (600 miles) due to the winds coming off the Pacific coast and heading east. Therefore, it's a tradeoff of where you want to deal with winds, the deserts of California and Arizona, or the deserts of West Texas.
One more slight reason to ride east to west - the eastbound riders I came in contact with that had left San Diego in March still hit cold weather and snow in Emory Pass in New Mexico in early April. Whereas by the time I got there, the weather (although I hit a nasty thunderstorm on my ascent) was in the 60s and 70s in the mountains.
I also rode east to west because I live in California and so each day I rode west I'd be one more day closer to home - kind of a psychological boost.