It seems like they both mean the same, young man. What is the difference between them?
According to this site: http://detail.chiebukuro.yahoo.co.jp/qa/question_detail/q1312853
少年 is used for persons till 20 years (or depending on the law from elementary school till 18 years)
青年 is used for persons from 14/15 years till 24/25 years.
Also you should take care, that 青年 and 少年 can be used for females, too. (See comments from eltonjohn and snailboat.)