I have used Moodle extensively and find it to be fairly easy to use and very full featured. You can also get it for free. I have seen a college demo of a sharepoint and it looked really cumbersome.
With Moodle you can run your whole class online if you would like (grades, discussions, assignments, etc.)
If you just want to upload a bunch of files then a wikispaces or edublog account might be even easier than Moodle. However, if you think you might want to have some online interaction or an online gradebook, then go for Moodle.
We use Moodle extensively at our K-12 school. It offers an easy learning curve, varied services, growing integration with other sites and being open source offers economic inclusion for a broad spectrum of environments . If you were to use a Moodle partner, I can recommend Remote-Learner with out hesitation.
Our system uses SharePoint for teacher sites and student digital portfolio. With the most recent upgrade in SharePoint, they have added blogs and wikis. The site works well for some teachers because most things are fill in the blanks and say ok. We are now beginning to learn code or find code to embed video, audio, picture shows, etc. I like having everything in one place. I really think this discussion can be narrowed down to your preference in look and feel.
SharePoint is a powerful system that is fantastic for document-centric collaboration. There are plenty of elements to facilitate online interactions, including surveys, discussion forums, and so forth. One of the coolest features is a/synchronous chat attached to individual documents. I also really like the easy versioning functions. If it is well-managed and well-supported, it is really fun to use. Additionally, it seems better when used on an intranet than on internet and, of course, if everyone is running IE and using the latest version of MS Office.
Now, for most people, these are too many restrictions. It works better for organizations with large IT departments and standardized setups.
Moodle is another beast entirely. Just like the other respondents say, its easy to use, set up, and it was built for facilitating online learning (whether it's really an LMS is debatable :) The basic set up is more than enough for most users and adding modules, learning objects, and outside services can make it into just about anything you need.
In the end, it's more likely that Moodle will suit your needs better than Sharepoint.