The thing kickboxing helps me with really is fighting from the outside, which someone mentioned. Also their is more of an emphasis on the head kick in western kickboxing as low kicks aren't allowed. Take note that I study a more European style (Dutch).
Since the rules are so much different between the two it's not really fair to compare them. If you took a Muay Thai fighter and put him in a western kickboxing match he would lose most of his weapons and advantages. Where as if you took a kickboxer and put him in a muay thai match he would be overwelmed with the strikes that are allowed.