Did the labor movement of the early 20th century fare any better than that of the late 19th?
That is a very good question, and you're likely to get a varety of assessments depending on the historian, but I would argue that labor unions fared better in the first decade of the 1900s, but only marginally so.
Despite continued backlash from corporations and the rich, including strikebreaking, employing spies and blacklisting, the number of people in unions increased at that time. So did the number of strikes and work stoppages. A handful of these ended favorably for workers, in no small part because progressive legislation was becoming more common, and most of all, government was becoming more directly (and neutrally) involved in labor negotiations.
Still and all, working conditions remained frightfully dangerous and miserable. Child labor was widespread in sweatshops and mines, and wages, despite limited increases, hovered near subsistence levels. The real advances in worker pay, rights and safety would not come until the 1930s and 40s.