The differences can be huge or can be slight depending upon whether the architecture of the curves is hugely different or slightly different.
I would not get too hung up on linearization results - but rather the actual final print results. Even from day to day, as the paper humidity changes and your print heads are not in the same condition as they were the day before, some variations are expected. What is important is that there is no visible crossover, or any posterization no matter how slight. While these same changes in conditions and print heads affect color printing as well - defects are infinitely easier to detect in a monochrome system. Very few people can actually observe differences in more than a handful of colors, while monochromatic variations are instantly recognizable. So do not spend all your time doing linearizations - it will drive you mad. If your eyes detect abnormalities - then you need to consider the problem. On the other hand, you may be well satisfied by having your printer "profiled" with custom curves - and those are available to you here:
For the test, you can be using the 21 steps but only if you do not modify it or convert it when opening. You should be printing it from QTR Print Tool if on Mac and following our QTR Print Tool workflow - or printing it from the QTR GUI from windows. Each time using the correct curve for a media. ANy of the X800 and X880 curve families are interchangeable even as their architecture is quite different.