Let me mention what I mentioned over there. The Civil War and Reconstruction likely had a larger social effect on parts of the South than the Industrial Revolution. In this sense, it is the thing that was more influential. At a localized level the CW/Recon. was a shift in political, economic, and cultural norms. In rural or agrarian areas the Industrial Revolution would have been less pronounced than in other, more urbanized areas.
However, I do think that overall the Industrial Revolution led to greater social change in America. It also led to significant changes across the spectrum in economics, politics, and culture, as likely in religion as well. Trade was made more efficient by the changes brought from the IR, America as a nation was able to prosper, and militarily it developed to the strong point it was at by the time of the Spanish American War. Simply put, I don't think that the Civil War/Reconstruction affected the entire nation in the same way that the Industrial Revolution did.