I was a little confused on the usage of both words and didn't know if they both meant the same thing like saying "kid" or "child" or whether there was some nuance between the two words. Is there a case when you wouldn't use one word in a certain situation?
I would say the difference is big.
First, 少年 is a rather stilted word used mainly in novels, formal speech, news articles, legal contexts, etc. Children themselves almost never use 少年 in informal daily conversations unless it appears in a fixed set phrase like 少年ジャンプ. In manga, there are a few adults who use 少年 even in informal situations, but they are usually fairly pompous speakers.
Second, 少年 refers only to boys roughly between 6 and 16 (although there is no strict borderline). 男の子 can refer also to a male baby and sometimes a male adult.