The bigger difference is not in the heat, but, in how the heat interacts with the meat you are cooking. The difference between how conduction, radiant and convective heat works on food, how the thermal energy transfers and the nature of the heat, to a lesser degree.
Anytime you are cooking on a smoker/live fire oven, you are looking at having a draft of heat, moving through the area where y the items you are cooking are sitting. This changes the effect of the heat on the surface of the food. Silverfingers amazing range notwithstanding, modern ovens do not have the same properties of a constant movement of air through the cooking chamber. Not only is the air moving, but, because we cook at temperature well below where a perfect combustion would occur, the warm/hot air is also moist. This aids in the creation of bark (as opposed to char), a better surface texture and moister meat. Now, many commercial ovens have convection as a feature, and if you ever get a chance to cook chicken in an electric convection oven, you will have some of the best textured chicken you will ever eat.
All non-convection ovens will have hot and cold spots, we never check on this, but, any experienced baker will know that their oven cooks unevenly. This is why all commercial bakers of cakes and pastry use convection ovens, and why breads from a wood burning oven are far superior to non-convection gas or electric ovens. Smokers that are drafting properly can have warm and cool spots, but, they are predictable, and the best cooks learn how to use those spots to their advantage.
A well seasoned oven is rarely as 'dirty' as a well seasoned pit. This makes a difference as well, if someone were to run their pit as a sparkling clean cooker, they would find that the cooks are not as good. The seasoning makes a difference, each pit has it's own smell, whereas a clean oven, necessary to prevent smoking or fire, will always lead to a cook with clean characteristics. These can be exploited as well, I love cooking in my oven, it is just another tool. If you put as much time into understanding your oven, and learning how to use it, it will yield excellent food.
Whip It Off, Chambers!
"perhaps...but then again...maybe not..."