What are common between them:
Both of them support Ajax and make it easier to use.
Both of them encourage the clean programming sytax in a way.
Since Dojo is a toolkit, it contains a lot more libraries such as animation or flash. On the other hand, Prototype is closer to the ground and often used as the actual codebase to develop a library or toolkit. For example, Scrip.aculo.us is developed on the base of Prototype.
Dojo appears to have better documentation but the Prototype community is working on creating better documentation.
My take on them:
Using a framework can make some work simpler but they may also cause other issues if you are not committed using them. That being said, both of the frameworks are nicely developed and useful. I guess the choosing of one over the other is based on where and how they will be used.