Who competed in the 1800's for industrial domination?
At the beginning of the 19th century, there was no competition -- Great Britain alone was industrialized, having became the first country in the world to do so and remained alone for a number of years. However, by the 1830's they were followed by Germany, which began to compete with Britain not just for industrial output and markets, but raw materials to feed their growing factories as well -- which drove the fierce competition for colonies between the Empires that eventually exploded into World War I a century later.
After Germany came the United States and France in the latter 1800's. These 4 countries represented the sum total of industrial nations by the outbreak of World War I in 1914.