No they are not the same. "May not" indicates assumption. This means that there is a possibility that another opportunity happens again or there is a possibility that it does not happen again. We simple believe that the possibility of the opportunity happening again is less likely to happen than the possibility of the opportunity not happening again. "Won´t" means "will not". Therefore, another chance is absolutely not going to accrue.

In the second sentence, you don't need 'another' AND 'again'. One of them is okay: We won't have another chance. OR We won't have the change again Otherwise, both sentences are okay, but the meaning is a little different: We won't have the chance again (definitely- the speaker is sure) We may not have the chance again (maybe- the speaker isn't sure)