ActionBarSherlock gives your application an action bar regardless* of what version of the android API your app is being run on. Action Bar Compatibility gives you the action bar only if the device that you're running on is API level 3.0 or above.
*Note that if the device you're running on isn't 3.0 or above, ActionBarSherlock is going to use it's own custom implementation of the action bar, not a native one.
It appears things have changed and there is actually no difference between ActionBarSherlock and the Action Bar Compatibility anymore. Please read the comments below for details.
After having used both now, I can say that I actually prefer ActionBarSherlock to Action Bar Compatibility. ActionBarSherlock is really easy and nice to use.
As LOG_TAG mentioned, there is now support for the action bar in the Android Support Library. I haven't had a chance to use it yet, but I would imagine that's the best one to use.