I have to disagree with Howard on one thing. There are plenty of NES and SNES games that play better with arcade controls, and even plenty that are exclusives, not just arcade ports. Aside from fighters, there are plenty of shmups that are much better with a stick, and I could make an argument for some of the tougher platformers.
However, I have to strongly agree with his other point, which is that the sticks and buttons on those things are very poor. It would be a ton of work to end up with something that as an actual controller is pretty mediocre. Unless this will be a novelty that sits in a display, I think the most important thing should be that it plays well. If you want a challenge, how about finding a way to use proper sticks and buttons. You could either find a way to mod those cases to fit them, or you could make your own replica case. It would play soooo much better.