“To find a better life” is the easy answer but an incomplete one. The European peasantry had lived through worse times than the mid-1800s but the period of 1850-1880 is when the largest share of Germans came to America. This is roughly the same time most of the Riedesels came to America.
A necessary condition for the mass emigration was increased opportunity to do so. German peasants were actual freer to come and go than in feudal times. A burgeoning transportation/emigration infrastructure of river boats, trains, safer trans-Atlantic ships, and emigration agents facilitated the movement. And the United States offered unprecedented economic opportunities. Rural areas such as Wittgenstein did not benefit from the industrialization and urbanization elsewhere in Germany, creating further economic disadvantages.
By the 1800s, strictly religious motivations for emigration were of limited importance. “Follow the money”, as they say.
My dear, late friend Karl-Ernst Riedesel of Berleburg wrote these notes on the topic for the benefit of an American delegation.