Personally, i think it is best to have 8 way sticks, as well as a dedicated 4 way, although that can lead to a cluttered panel. If you aren't going to build dedicated cabinets, you have to compromise. If you really want a single stick to play them all, you have to decide on how much effort you want to put into it.
The U360 is smooth, silent, and very versatile, however they are expensive, and dont feel like the joysticks you remember using in actual arcade cabinets. They are fully automatic though, you don't need to worry about switching anything.
The Ultimarc J-Stik (Sanwa JLW) is an awesome option as well. It is much cheaper than a u360, and has microswitches and a physical restrictor plate. I recommend the ultimarc version since it is modified so that you can rotate the restictor plate without loosening any screws. It has a square gate so the corners are easy to hit in 8way mode, and when rotated, it makes an amazing 4 way stick. With it being square, it makes a decent qbert stick as well. ( just set the game to move when two switches are activated). The big downside to this stick is you have to physically rotate the restrictor from the bottom of the panel, which is inconvenient....which leads me to the:
Ultimarc Servo Stik: This is a motorized JLW, so it has all of the benefits of a JLW, but it switches automatically so you don't have to manually rotate it. Once again, it isn't cheap, but it might just be the best option ever.
I currently have U360s in my 2 player cabinet, and J-Stik/JLWs in my 4 player cabinet. I fully intend on purchasing the servostik upgrade kit when i have the extra cash for the p1 stick in my 4 player cabinet.