Anything you want to braise should be done in a dutch oven. It will turn out much better than a slow cooker. The surface is allowed contact with air that's hot enough to give you a maillard reaction which does not happen in a slow cooker. It's also much more convenient because you can brown meat, cook down onions/garlic/etc., in the same pot that you thrown in the oven on low temp to "set and forget". With a slow cooker, you need to dirty a pan and the slow cooker.

Some of our typical braises are barbacoa, short rib ragu, gumbo, chicken tinga.