Braised short ribs differ in texture when on stove top vs in oven I've made braised beef short ribs several times previously and I've found that when they're braised on a low flame in a cast iron pot over the stove, they ended up being more tender compared to those I left in the oven in the same cast iron pot. 

In both cases, the pot was covered with a lid, the braising liquid was essentially the same in composition and volume, the cooking times were the same (four hours) and the ribs were from the same butcher. The temperature of the braise seemed to be the same as they were at a very mild simmer in both cases. 

I understand that a pot on a stove would receive heat primarily from the base of the pot while a pot in an oven would be exposed to heat from all directions. However, seeing as how in both cases the ribs were completely submerged in liquid, I figured that the direction of the heat source should not matter enough to cause differences in the texture of the meat. 

Does anyone have any idea what else might be causing the difference in texture?
"For the same time" seems to be your problem here. An oven will warm a pot much more slowly than a stovetop, especially a heavy iron stew pot. You'll need to monitor your temperature, and only count the time after it reaches 68 Celsius. The warming up phase can be easily close to an hour in the stove, eating away a lot of the actual cooking time.