Some lathes chuck mounts are better than others. The Hardringe system is very accurate and repeatable with the longer taper and 1/4 turn locking it. With a dedicated chuck it repeats within .001 and a good chuck ground to the spindle will be very accurate. We had 4 Hardringe lathes in the tool room at work with chucks dedicated to them ( other than the 6 jaw) The draw back to the hardinge mount is it doesn't take fast reversing of the spindle as good. Keeping the chuck clean and in good shape makes a big difference. Another is not to over stress the chuck tightening it, this springs the scroll and makes it loose accuracy