Marx, a German who lived from 1818-1845, saw the industrial revolution as a force that reshaped individuals' relationship to the work setting, specifically separating the worker from his ultimate product. It reduced craft to labor by exploiting the worker as a cog, dehumanizing large percentages of humans.
Weber saw people as effected by economic realities, as responding to social position (prestige) but as harbingers of ideas that could affect their own behavior. He specifically felt that moral attributes such as a work ethic and frugality contributed to social movements.
Marx distinguished workers in the industrial revolution from pre-industrial worker (most agricultural) in which the working class had a full relationship to the product (or outcome) of his toil, in which workers had a steady interaction with their environment (as farmers or merchants). In other words, a farmer lived and worked on the same soil, raised animals from birth to maturity, and lived in a natural world where seasons governed his movements and responses.
This dehumanization posed by factory work changed society radically and exploited individuals economically. Marx viewed humanity both idealistically and realistically, acknowledging the reality of a capitalistic system but disparaging it for its ultimate inability to sustain itself. He essentially saw individuals as caught up in sweeping economic forces over which they had little control.
Weber, a sociologist who lived from 1864 to 1920, had a view of humanity that was based on moral imperative, viewing human behavior through the lens of ideas. Great ideas, such as Protestantism, combined with economic forces to drive changes in society. He trusted that human behavior was governed to a large extent by over arching ideas such as moral fortitude and frugality, governed by philosophies represented by symbols. People's response to symbols (such as their countries flag) was proof the individuals responded to forces beyond the economic.
Weber did not believe that governments had much effect on personal philosophy, but that class and status did, since people responded to ideas such as religious principles. Marx, on the other hand, saw humanity swept up in events in which dynamics of power and economic inequality exploited the weak. Thus, huge numbers of people had essentially no choice, as they lives were spent in servitude.
Marx's prediction that capitalism would ultimately fail due to the "withering of the state" was incorrect; however, his observation that capitalism is unsustainable is proving correct in the inability of human beings to solve environmental problems that may lead to worldwide collapse. He correctly viewed humans as efficient machines of production, which has led to overpopulation, which threatens their ability to sustain resources.
Weber's view of the industrial revolution—that it is governed by an idea, such as the promise of technology; the virtues of Protestantism—didn't fundamentally regard people's interactions with one another, or the state, as economic. Marx viewed a larger, sweeping arc of human development; to him, status was less important because most humans (workers) were exploited and even though some (the owners) had wealth—the system ultimately ruined (dehumanized) all classes. Status only mattered if you had power, or didn't—and even then, both sides were ultimately cogs in a machine meant simply produce and consume.
Marx saw the state as becoming more and more intrusive in people's lives. His analysis was correct but his solutions are flawed. Weber correctly interpreted individuals as acting in interests beyond the economic, and in predicting the rise of a middle class, but he failed to fully acknowledge the power of governments and economic structures to shape individual's beliefs through manipulation of information (media) and the inertia of maintaining the status quo (the tendency of the powerful to hold onto their power).