Beginners often use the crop on the horse's shoulder because it is easier to do. In order to use the crop behind your leg, you have to take the reins in one hand and reach back with your other hand to use the crop. So it takes a bit more skill. But it is always preferable to use the crop behind your leg because it makes more sense to the horse. After all, you are using the crop because your horse didn't respond to your leg, so you want to use your crop right behind your leg so your horse connects the two. Experienced lesson horses generally are quite aware when they're being bad, and if you whack them on the shoulder they know exactly why they are being hit with the crop. But many other horses wouldn't realize that they got hit on the shoulder because they ignored your legs and didn't go forward. Besides, since impulsion and energy come from the horse's hindquarters, it makes more sense to hit him behind your leg. The only time tapping the shoulder with a crop is really effective is when you are trying to correct a horse dropping his shoulder and scooting sideways. Then the crop tells the horse to pick up that shoulder, and is not used to make him go more forward.
I don't know much about Western, but in English disciplines judges will expect you to use your crop behind your leg. In a beginner class they might overlook it if you use the crop on the shoulder, but it very much marks you as a beginner. Tapping on the rump is not something you should do at a show at all. I have seen some dressage trainers tap the rump for specific purposes, like to get a horse to lower his croup when teaching piaffe in hand. You generally hold the crop in your inside hand (so you have to switch hands when you change direction.) But if your horse tends to ignore one leg more than the other, or like to run out to one specific side, you may keep the crop in that hand all the time.
People who tell you that good riders don't need a crop are just ignorant. My old dressage trainer used to require that all riders carry a whip at all times when mounted. After all, just because you carry it doesn't mean you EVER need to actually use it. But if you ever need it, you have it ready. Better to tap your horse with the crop/whip the first time he tries to ignore your leg and fix the problem immediately than to keep kicking and kicking until your horse's sides are dead.