Is there any distinction between 二百 (èrbǎi) and 两百 (liǎng bǎi) which both mean "two hundred"?
This is more idiolectal. I personally use more 两百, which are also the preference of the most people I met within so many years.

However, in some context, it should be fixed. For example, we say someone is 二百五 which  means someone is an idiot. In this context, 二百五 sounds idiomatic.