What Danielg said is good. I would add:
If you watch the videos about System.Addins, they are clearly talking about very large projects. He talks about one team managing the host application, another team managing each AddIn, and a third team managing the contract and the pipeline. Based on that, I think System.Addins is clearly for larger applications. I'm thinking applications such as ERP systems like SAP (maybe not that big, but you get the idea). If you watched those videos you can tell that the amount of work to use System.Addins is very large. It would work well if you had a lot of companies programming 3rd party add-ins for your system and you can't break any of those add-in contracts under penalty of death.
On the other hand, MEF seems to share more similarities to SharpDevelop's add-in scheme, the Eclipse plugin architecture or Mono.Addins. It's much easier to understand than System.Addins and I believe it to be a lot more flexible. The things you lose are that you don't get AppDomain isolation or strong versioning contracts out-of-the-box with MEF. MEF's strengths are that you can structure your entire application as a composition of parts, so you can ship your product in different configurations for different customers, and if the customer buys a new feature, you just drop the part for that feature into their install directory and the application sees it and runs it. It also facilitates testing. You can instantiate the object you want to test and feed it mock objects for all its dependencies, but when it runs as a composed application, the composition process automatically hooks all the real objects together.
The most important point I'd like to mention is that even though System.Addins is in the framework already, I don't see a lot of evidence of people using it, but MEF is just sitting there on CodePlex supposedly to be included in .NET 4, and people are already starting to build lots of applications with it (myself included). I think that tells you something about the two frameworks.