Basically, the situations and the attitudes towards the issue of slavery were different at these two times because 10 years of events had happened to drive the North and South farther apart politically and on the issue of slavery.
In 1850, there were many divisive events that had yet to happen. The Compromise of 1850 was new and the Fugitive Slave Act had yet to become the huge source of conflict that it was soon to be. Uncle Tom's Cabin, written partly because of the Fugitive Slave Act, had not yet been written. The Kansas-Nebraska Act had not yet been proposed and therefore the horrible conflicts of "Bleeding Kansas" had not happened. Brooks had not yet beaten Sumner. Roger Taney had not yet declared that Congress lacked the right to legislate on the issue of slavery in the territories.
All of these things would cause the North and South to become more and more estranged from one another. This caused the political situation and the attitudes towards the issue of slavery to be very different in 1860 than it had been 10 years earlier.