An American cotton plantation owner would typically have seen the rise of Britain as a good thing. The reason for this is that the rise of Britain would have benefited him by creating a market for his crop.
The rise of Britain by 1850 was based largely on textiles. It was the factories of Manchester and other English cities that gave Britain the most powerful economy in the world. These textile factories needed huge supplies of cotton to keep them going. This, of course, created a huge opportunity for American cotton plantation owners. With the factories of England demanding cotton, they were able to ramp up their production (using, of course, slaves to do the work). This made them rich and influential as a class. Therefore, our hypothetical American cotton plantation owner would have seen the rise of Britain as a boon to him.