The Missouri Compromise went out of its way to make sure that the supremacy of the Federal government wasn't compromised in any way by the new state. After all, that was supposedly the whole point of Congress creating a fuss over the addition of Missouri.
First and foremost in the minds of Congress was the need to not upset the carefully constructed authority of the federal government of the states…because that would harken back to the Articles of Confederation. Nobody wanted that, not even the staunchest states rights advocates at the time.
Congress was eager to expand the Union, but was super-careful in doing so. It was necessary to ensure that the fundamental integrity of the Supremacy Clause wasn't undermined by the right of self-determination by new states.
Section 7 of the Missouri Compromise (mandating Congressional approval for Missouri's constitution) was arguably the most important factor of the Compromise's place in U.S. history: It set a legal precedent that allowed the federal government to retain all final say on state constitutions.
While the Missouri Compromise was super-concerned with maintaining the power of the Federal government, it was ultimately about ensuring states' rights.
In fact, the states' rights issue was what people insisted the Missouri Compromise was all about. The drafters transformed what was clearly a slave vs. free state issue into one of federal vs. state power. The history of this struggle in the U.S. is fairly one-sided in favor of the federal government…but here at least the states' rights folks gained some headway.
While in the short run it seemed that the Missouri Compromise favored the federal government fairly heavily, the precedent for self-determination would later be used by the Supreme Court to rule that the Federal government had no right to interfere with a new state's fundamental right for self-determination.
Despite the ground made by the Missouri Compromise towards securing state rights, this was only a hiccup in the slow and steady march toward a United States in which Federal power would trump state rights in pretty much every way.
It should come as no shock that perhaps the single most fundamental theme of the Missouri Compromise is, well, compromise.
While the majority of this compromising was between factions within Congress, it was also between the federal and state government. The Feds gave a little in granting state status and in allowing self-determination, while Missouri gave a little in allowing Congress final say on the content of their constitution.
The compromises between state and federal power within the Missouri Compromise represent one of the great successes of the American system of checks and balances, allowing state and federal power to coexist within the rule of law.
The imbalance in bargaining power between the state of Missouri and Congress resulted in a slightly lopsided series of compromises. The Federal government won out, despite making numerous concessions to the state of Missouri.