If memory serves the original atari yokes used 10K pots. Incidentally I think a lot of other games used those too, some used 5K perhaps.
Most arcade analog controls I've researched use 5k pots but the resistance value isn't the main consideration
UNLESS it is wired in a 2-wire (variable resistor) configuration.
As long as it is wired in a 3-wire (voltage divider/potentiometer) configuration, the important considerations are the taper ("linear 1" FTW), quality, and condition of the pot -- a dirty/rusty old Radio Shack el-cheapo is

but a nice, long-life Allen Bradley or a Honeywell/Clarostat RV4 series is

.

I notice that in some games I get nice smooth movement and others I'm moving in steps. SW Trilogy is one of those, I move in steps rather than a nice smooth track and it makes me miss some shots. A few MAME titles exhibit similar, even tho I've gone into mame and supermodel and adjusted the values for each.
I'm wondering if this is a game thing or a hardware thing, or an emulator thing.
If you're getting smooth motion in some games, the encoder probably isn't the problem
unless there are more than 256 x 256 analog positions in the game.
IIRC Jon down-scaled the KADE's A/D conversion results from the 32u4's native 10-bit (1024) to 8-bit (256) position data to fit into the HID data-word size without adding another byte. (Apologies in advance if I messed up this description, Jon.

)
If the number of possible positions isn't causing the problem you are probably looking at either emulation limitations/errors
or not enough computing horsepower.
Would changing over to 100K pots help, in theory post calibration that would give ten times the steps for a game like Tril, if it is a emulator issue.
Nope. Remember that pots are analog, so there aren't 10x more "steps" in a 100k pot vs. a 10k.
The pot acts as a analog voltage divider and the encoder's A/D converter samples the analog voltage and converts it to to an 8-bit position. (~19.5 mV/step or 1.05 degrees/step)
If you need more steps, change the source code so your encoder outputs a 10-bit position. (~4.88 mV/step or 0.26 degrees/step)
Unless the wiper arm and/or resistive element of the pot are dirty/corroded/worn, changing pots will not help.
Scott