For fast cooking meats, like steaks and tender roasts, the final temperature is the determiner of how well done the cut is because the doneness is directly related to which proteins have denatured. As the temperature increases, more of the several types of proteins have been effected. This process concludes around 165 F / 74 C when the meat is well done.
All low and slow dishes, whether braised, barbecued, or slow roasted are cooked well past the point of being well done.
Therefore, the internal temperature is less a guide to how well done they are and what the final texture is like.
These types of slow cooked high connective tissue cuts like beef chuck or pork butt require time at temperature because the conversion of the collagen to gelatin takes place over time, with the process proceeding more quickly the higher the temperature.
For large cuts done very with dry barbecue methods, this could take 12 to 18 hours; for smaller cuts done in the oven or braising which achieves a higher temperature, it could take only 3 or 4. The size of the pieces also matters, as it takes time to heat the pieces through to the center, which is why stews where the meat is cut into chunks can be done in only a couple of hours.
The very best test for doneness when doing low and slow cooking is therefore to check the texture directly. Try cutting the meat, or pulling it apart. If it is not yet as tender as you desire, continue the cooking.
That said, you may find that the final internal temperature when done to your liking has risen as high as 200 F / 93 C or so but this is not necessarily so.