I've used both the Mag-Stik Plus and J-Stik with servos.
Mag-Stik: I really like the short throw feel of the Mag-Stiks, but you may not like that. Also, what @millercentral said about guests is true. Not many can figure out very easily how to switch them. You have to do it for them.
J-Stik: This is a copy of the discontinued Sanwa JLW with some springs to help you turn the restrictor plate easier. I've created a mod to allow me to use them with RC servos in my cocktail cabs. It works very nicely. I'm sure Andy's new servo-stik is very similar in operation, although he's created a custom restrictor plate, while I modded the existing one. I'm sure his new ones have been well tested though. The J-Stik has a much lighter feel, and longer throw than the Mag-Stiks. I found they took some getting used to.
U-360: I can't comment too much on this, as I've never tried it. It's again a modified J-Stik (JLW), with no restrictor plate. I think that would really take some getting used to. I personally like the feedback you get from the plate.
If at all possible, I think your best bet is to find some people with these installed and try your favorite games on them. Save yourself the expense of ordering something and finding out you don't like it.
Regardless of the stik you choose, you can't go wrong ordering from Andy.