I'm sure others can tell you more of the science behind it.
Fat content is one factor, but there are others as well. The texture of the meat, the type of meat (fowl, fish, beef, etc.), the method of cooking (frying, broiling, grilling, roasting, etc.), spices and other ingredients used along with the meat.
Take a small beef steak for instance. You will get totally different flavors if you fry, broil, grill, or boil it (yuck on the last one!). A medium-rare steak tastes different than a well-done steak.
Chicken can be fried, roasted, boiled, grilled, etc. Each method changes the texture and the flavor.
Some spices and condiments go well with one meat and not so well with another.