Most braises do better in the oven than on the stovetop (with a few exceptions, like quick vegetable or seafood braises). The reason oven braises work so well is that even heat from all sides surrounds the pot, leading to gentle, even cooking and a flavorful liquid that becomes the sauce.
The heat of a stovetop burner, on the other hand, is too focused. With stovetop braising, the heat concentrates on the bottom of the pot and can easily overheat the starch in the liquid, which breaks down its thickening properties and thus results in a thinner sauce.
For the best braising, you’ll want a sturdy, roomy pot with a tight-fitting lid. We often turn to an enameled cast-iron Dutch oven as our preferred vessel because they retain heat well, are easy to clean, and transfer easily from stovetop to oven. Depending on the recipe, a stainless steel skillet is also a good choice.