Braising is long cooking at lowish temperature in liquid. The idea is to tenderize tough meat without overcooking by keeping it mostly immersed in liquid (which won't go over 212F). The long cook will tenderize tough cuts like oxtail. You would destroy a tender cut like tenderloin.
I like a pot in the oven because you know what temp it is and who knows what temp a slow cooker gets to?
A secondary benefit is that you can build a sauce with the liquid. I like short ribs braised at 250F x 3 hours in red wine/garlic/onion/carrot/soy and a spoon of tomato paste.. you can let t he meat rest in the sauce which makes it taste better and then reduce the liquid for serving.
