You should scroll down this page and you will see that that question has been asked and answered at least a dozen times! It is a common mistake to confuse the two when they are young but as adults the differences are striking. The childrens grows from 2 to 3 feet, while the spotted grows from 3 to 3.5 feet (rarely 4 feet). They have basically the same temperment which is wonderful in both. The biggest difference is that the childrens loses its pattern as an adult and becomes a solid tan color. The spotted on the other hand keeps its pattern and becomes more and more beautiful as it grows. "Cape York spotteds" are the most beautiful snakes in the Antaresia genus (which include childrens, spotteds, stimsons, and anthill pythons). To make a long story short, if you want a nice little brown snake, get a childrens. If you want a beautiful little snake, get a spotted. Their husbandry and caging requirements are almost identical.
Search on google for pictures of both or go to breeders' websites.
Hope that helps!