Alpha = 100% testnet and monopoly money. Beta = Likely to be in the testnet for the first phase and then move to the main-net (with real stake and coins). It is still undecided whether nemesis block is on launch day or in beta. It doesn't make much difference imo.

NEM Beta will include some special features. Even NEM open Alpha will likely include special features that are not in other coin's launch. For example: NIS codes for secure messaging have been completed and just need GUI to be on Open Alpha. Secure messaging is not even in Nxt NOW 9 month after the coin launch. Talk about the difference between one system's alpha and the other system's so-call advanced stage.

NEM beta will include features that have never been in any other system. What are they ? We cannot tell you because the codes are not completed and there are some uncertainty in the implementation. However, there will be at least one special feature moving from NEM Alpha to NEM Beta.