Steel-cut oatmeal is a whole food, containing all the edible parts of the oat grain. Oat bran is a fraction of that whole grain, but arguably the best part (it's missing the germ, which contains vitamin E and some other vitamins and minerals, and the endosperm, which basically just contains carbs and calories).
I like both, but have tended more towards oat bran because it is so fast to make (2 minutes of cooking, vs 1/2 hour for steel-cut oats). I also like to mix it with other whole grains, like amaranth or quinoa or teff--I cook the whole grain in the amount of water needed to cook both the whole grain and the oat bran--no chance of the grain sticking, because it's in extra water--then the last 2 minutes of cooking time, I toss in the oat bran).