both the Missouri compromise of 1820 and the converse of 1850 settled conflict between the north and south over what issue

Slavery

Explanation:

Their main issues were trying to figure out what states were slave states and what states were free states.

By September, Clay's Compromise became law ... Finally, and most controversially, a Fugitive Slave Law was passed, requiring northerners to return runaway slaves to their owners under penalty of law. The Compromise of 1850 overturned the Missouri Compromise and left the overall issue of slavery unsettled.