Ultimately, this question refers to the political and economic realities taking shape under the Gilded Age, when business operations were getting larger and larger, as the United States transitioned into the Industrial Age. The thing to keep in mind about this era is that it was defined by laissez-faire capitalism,...
Ultimately, this question refers to the political and economic realities taking shape under the Gilded Age, when business operations were getting larger and larger, as the United States transitioned into the Industrial Age. The thing to keep in mind about this era is that it was defined by laissez-faire capitalism, and there were no regulations in place to protect the rights of workers as there are in today's United States. Poor wages, dangerous working conditions, extraordinarily long hours, child labor: these were all common to the time period in question.
In some respects, the most difficult part of your question to address is the subject of unionization. Unlike the Populists and the Progressives (which tend to reflect specific political movements), there were multiple approaches and organizations which have collectively shaped the history of labor in the United States. The earliest national unionization movement (The National Labor Union), for example, looked towards political action in a way more reminiscent of Britain's Labor Party than what would become the norm in the American context. Both the NLU and the Knights of Labor (founded in 1869) declined, however, and the labor organization which would ultimately prove most effective was the American Federation of Labor. In addition, you'd need to differentiate between Craft Unionism (like the AFL, which is specifically aimed at Skilled Workers) and Industrial Unionism, which embraces all workers within a given industry. The basic idea of unionism, however, remains consistent: there is a fundamental power imbalance between workers and employers, and through the use of collective action and mobilization, unions seek to correct that imbalance.
By contrast, the Populists and Progressives were both political movements, based in government action. The Populists were based in agricultural communities, and while they did try to get reforms in line with working class interest, their main appeal remained in the farming sector. Their most famous reform called for the adaptation of silver currency, to increase inflation (a policy which would be to the benefit of farmers, who would be able to command higher prices and more easily pay off their debts). In addition (among other reforms) they called for a graduated income tax, and various political reforms to increase new levels of democratization into government. The Progressives adopted some of the Reforms first championed by the Populists, and were largely focused on passing legislation and devising solutions which would address and correct some of the fundamental shortcomings of society around the turn of the century. As an example of Progressivism, consider administration of Theodore Roosevelt, during which time the Pure Food and Drug Act was passed, and under whom the Federal government began applying anti-trust laws against Big Business interests (a policy which Taft would expand far beyond Roosevelt's deeply pragmatic sensibilities).
This represents a very basic overview to the key subject matter your question addresses. From here, you would need to look further into the historical record, to compare and contrast which of these groups was most effective, and come up with a rationale for why.