HR, I have a CH Products Flightstick, all with default settings, and it's fine for me. I'm wondering if the wobble you are talking about might be the inertia effects in the flight model.
In Air Warrior, there were no complicated effects dependent on angle of attack, so when you pulled back a little (but quickly) on the stick, the nose generally would move up a little quickly, in a straight line, and stay there. In Aces High, there are all sorts of more-complicated, more-realistic flight dynamics modelled so that, when you pull back a little but quickly, you should notice the nose do more than move up quickly in a straight line and stay put. It depends on the plane, but many will have the sight move up quickly but oscillate slightly, briefly up and down and sometimes even side to side a little.
The magnitude and duration of the osciallation generally aren't large -- maybe a second or so and amplitude of half a gunsight or less. It depends on the plane, too. However, it is enough to need getting used to compared to Air Warrior, and it contributes to the aspect that, in transitioning from Air Warrior to Aces High, gunnery takes the longest in which to become proficient.