I think the difference is more subtle than what you're making it out to be.
Once the national government has become abusive of its power, it has abrogted the constitutional contract it has made with "the people." Had the states of the South gone to the state legislatures to garner approval, would that have been sufficient? Something tells me that you would still not be happy.
No, that wouldn't have been sufficient. As a matter of fact, I am under the impression that is what occurred. The states that seceeded held conventions made up of their state representatives. The Constitution is a national and federal government. That is why there is a US Congress. That is the national body of the people.
The questions of secession--may it be permitted and shall it be permitted--belong to the national government, first to the Congress, and, if challenged, to the Supreme Court. To my knowledge, even though these questions were clearly a controversy between the states, the question was never tested according to the Constitutional means provided. There was a presidential election. The slave states did not care for the outcome. And so they forced the issue.
It was the all the people--nationally--who ratified the Constitution. They did so, however, in the form of the several states, as Madison liked to say, "acting in their most sovereign capacity", which is to say, by the representative will of the people. But as Madison has pointed out:
I return my thanks for the copy of your late very powerful Speech in the Senate of the United S. It crushes "nullification" and must hasten the abandonment of "Secession." But this dodges the blow by confounding the claim to secede at will, with the right of seceding from intolerable oppression. The former answers itself, being a violation, without cause, of a faith solemnly pledged. The latter is another name only for revolution, about which there is no theoretic controversy......The Constitution of the U.S. being established by a Competent authority, by that of the sovereign people of the several States who were the parties to it, it remains only to inquire what the Constitution is; and here it speaks for itself. It organizes a Government into the usual Legislative Executive & Judiciary Departments; invests it with specified powers, leaving others to the parties to the Constitution; it makes the Government like other Governments to operate directly on the people; places at its Command the needful Physical means of executing its powers; and finally proclaims its supremacy, and that of the laws made in pursuance of it, over the Constitutions & laws of the States; the powers of the Government being exercised, as in other elective & responsible Governments, under the controul of its Constituents, the people & legislatures of the States, and subject to the Revolutionary Rights of the people in extreme cases.
It might have been added, that whilst the Constitution, therefore, is admitted to be in force, its operation, in every respect must be precisely the same, whether its authority be derived from that of the people, in the one or the other of the modes, in question; the authority being equally Competent in both; and that, without an annulment of the Constitution itself its supremacy must be submitted to.
The only distinctive effect, between the two modes of forming a Constitution by the authority of the people, is that if formed by them as imbodied into separate communities, as in the case of the Constitution of the U.S. a dissolution of the Constitutional Compact would replace them in the condition of separate communities, that being the Condition in which they entered into the compact; whereas if formed by the people as one community, acting as such by a numerical majority, a dissolution of the compact would reduce them to a state of nature, as so many individual persons. But whilst the Constitutional compact remains undissolved, it must be executed according to the forms and provisions specified in the compact. It must not be forgotten, that compact, express or implied is the vital principle of free Governments as contradistinguished from Governments not free; and that a revolt against this principle leaves no choice but between anarchy and despotism.
Letter to Daniel Webster, 1833
Anarchy and despotism, he says. You see, it is the people who gave the Constitution its authority, which, so long as it remains in force, is supreme. Madison mentions two scenarios whereby a state may remove its constitutional obligation: annullment or revolution. The Constitution was not annulled. Therefore, the only Constitutional context for the actions of the slave states was revolution. As I have said, they are judged by history as to whether their case was justifiably extreme or not. They fail that test completely.
Madison's letter to Daniel Webster is a great read. Like a Rosetta stone of the secession question. By the way, the speech Madison praises Webster for is his Second Reply to Haine. You should read it if you haven't.