You can do either but oven is better because it's a more stable environment. You can set it and walk away. Same with cooking beans. On the stove top you need to stir occasionally but not in the oven because the heat is coming from all around and not just the bottom of the pot.
Both.... Brown your meat (or not meat if you're a veg...) in a heavy dutch oven on the stovetop, add your liquids and bring to a simmer. Then, cover and move to a moderate (275-325) oven to finish. For "braising" fish or veggies, you can get away with doing it all on the stovetop. For long and slow meaty-type dishes, the oven is best for all around ambient heat.