If I remember well, xbox 360 pads have those sticks with two orthogonal pots, one for each axis, wired in parallel. If you change one of the two axis pot (100 K ohm) with a different value pot, it will not work correctly.
Pretty sure that XBox 360 used 10k pot thumbsticks.
Maybe what you're describing relates to some of the older controllers that didn't have a "Common Ground" setup, but I haven't found anything that confirms it.
BadMouth tried other value pots for a newer XBox 360 padhack w. twin analog joysticks.
This post mentions having more jitter problems with 5k pots than 10k or 50k.
Ohm's Law shows that using different value pots would cause a difference in the amount of current flow for a given voltage.
Voltage (V) = Current (Amps) * Resistance (Ohms)
5v = 1mA * 5k Ohm
5v = 0.5mA * 10k Ohm
Even if you wired a 5k and a 10k potentiometer in parallel, both would still act as voltage dividers.
The 5k pot would draw twice the current as the 10k, but the A/D circuit in the encoder would still be measuring the wiper voltage.
If it was measuring resistance or current flow, the 5k and 50k pots wouldn't have worked in BadMouth's tests.
Scott