OAuth 1.0 and 2.0 are two completely different protocols. However, they are designed to solve almost the same basic set of use cases, and most people developing the new version have working versions 1.0. Therefore, they all made sure that it would be trivial to update.
With 2.0, you get more options when it comes to how you want to issue authentication access tokens. Suppliers with support at the beginning of 2.0 use Bearer tokens, which are sent via HTTPS and do not include cryptography on their own. Another (much better) option is to use MAC tokens, which are similar in design to OAuth 1.0 HMAC-SHA1, but are easier to use (there is no normalization of crazy parameters).
The main difference and where the transition can be more complicated is to deal with large scales. 2.0 handles a scale much better than 1.0 (which actually sucks on it). Therefore, if you need to scale, 2.0 will make your life much easier, but to take advantage of it, you will need to do some work.