Hi Byrna,
I fly MS FS all the time and I have the exact same problem. It seems to be just an inherant problem with FS, even with pay ware add ons.
The problem, as some have said earlier, is not the sensitivity, but the resistance feedback coming from the joystick. Not sure about other makes, but the MS Force feedback joysticks(which I thought would be the most compatible in relation to this) definitly doesn't do it correctly.
The best way of dealing with this is to go to your joystick sensitivity settings on FS and turn all three down. Don't be surprised if you have to turn them down a lot to get the desired result. I find that you need to turn down aileron sensitivity a little more than the elevator. You shouldn't have to turn the rudder down too much.
Also, turn up the null zone value. This will allow you a certain amount of lee way if you accidentely move the joystick slightly and help reduced the "pilot induced ossilations" that you speak of. God knows I've had enough of them
There is also a shareware program called FSUIPC. This program allows a lot of integration of 3rd party programs. It can also calibrate your joystick for a specific FS setting. Very handy. FSUIPC also has weather settings that allow you to smooth out the transitions in weather changes. This won't help you trying to land in a storm though. As I've said before FS can't model up or down drafts in the air. The way it deals with this is by reducing the wind speed to create a loss of lift or vise versa for an updraft. Unfortunatly, if you're trying to landing in a strong crosswind, this will lead to a severe yawing effect and nearly always requires aileron intervention to get back on track, even though you're not really supposed to do that.
As regards X-Plane, I've never used it, but any simmers that I know of that have used it say it is a giant step in terms of flight dynamics and air modeling in comparison to MSFS.
Anyway, hope this helps.
Cheers!