Let me assure you that playing a simulation game with a wheel IS better than with a controller. It simply is. I am talking about simulations games like Forza or whatever. Try to counter-steer with a controller to control your drift, let me know how it goes.
Same for Shmups, using an arcade stick is 10 time more precise than using a controller, it is so easy to evade bullets with a good stick.
Fighting games also can benefit greatly from an arcade stick. Pulling out combos is easier.