What's the difference between 128 microstepping and 1-1/64 microstepping?

I'm not sure what particular devices you're talking about so I can't help you as far as compatibility goes, but a microstep fraction refers to the resolution of the rotating motor. let's say your motor takes 200 whole steps to make one complete revolution of the spindle. If you then set your motor to run at 1/64 microsteps it would mean your motor is taking 64 times more steps to cover the same distance, making a total of 12,800 steps to make one complete revolution of the spindle. So a smaller fraction of steps like 1/128, would take even more steps to complete one revolution, 25,600 in fact. If you're talking about motor drivers it's probably telling you how many options of resolution you have. one giving the highest resolution of 1/128 microsteps but probably still capable of doing 1/64, 1/32, 1/16, 1/8, 1/4, 1/2 and 1 whole step. the other one that says 1-1/64 is telling you it ranges between 1 whole step and 1/64th microsteps, so you could do the fractions between like 1/32, 1/16, 1/8, 1/4 and 1/2 as well. The amount of microsteps you want to make in one revolution is totally up to you, more steps potentially means a more precise machine, but at a certain point the extra steps may be unnecessary. hope this helps