Hi There,
Live centers are used for general and high speed turning. But all live centers will have some TIR. Depending on the quality and condition of the live center, it usually is in the tenths of thousants of an inch but it is there.
A dead center cannot have any TIR and hence is more accurate (of course depending on its condition too). But this is only necessary for the finer classes of work.
Long ago, There were no tailstock live centers and when they were developed, they were expensive and not as accurate. Nowadays, they are cheaper (comparatively) and accurate enough for most classes of work.
Good Luck!
-Blue Chips-
Webb