The only real difference between the US and CS constitution when it came to state's rights was that the CS constitution denied the states the rights to ever abolish slavery, so it actually gave the states less rights than the US one.
Technically speaking, the Confederate Constitution did not deny the states the right to abolish slavery. Yes, it says "No bill of attainder, ex post facto law, or law denying or impairing the right of property in negro slaves shall be passed" but that is in the context of the portion of Article I which deals with the powers of Congress, not of the states.
https://avalon.law.yale.edu/19th_century/csa_csa.asp When the Confederate Constitution wants to limit the powers of the states, it uses language specifically referring to the states: " No State shall enter into any treaty, alliance, or confederation; grant letters of marque and reprisal; coin money; make anything but gold and silver coin a tender in payment of debts; pass any bill of attainder, or ex post facto law, or law impairing the obligation of contracts; or grant any title of nobility." Note that this passage does not say anything about the "right of property in negro slaves."
However, while a Confederate state could forbid its own citizens from owning slaves, it could not forbid citizens of other Confederate states from "transit or sojourn" in the state with their slaves: "The citizens of each State shall be entitled to all the privileges and immunities of citizens in the several States; and shall have the right of transit and sojourn in any State of this Confederacy, with their slaves and other property; and the right of property in said slaves shall not be thereby impaired."
https://avalon.law.yale.edu/19th_century/csa_csa.asp#a4 "Transit" implies something short-term but "sojourn" can last for a long time as long as you do not announce your intention to become a permanent resident of the state. What the Confederate Constitution did here was to make explicit a "right" (like the right to take slaves into the territories) which southerners believed was already present in the US Constitution; and as the Dred Scott decision had supported their position on the territorial issue, the US Supreme Court, had the ACW not broken out, would probably have supported their position on this issue. As I wrote some time ago, " What was more likely and more insidious was the possibility that the court would establish slavery in the North
gradually by first recognizing slaveholders' rights briefly to pass through northern states with their human "property"
https://en.wikipedia.org/wiki/Lemmon_v._New_York and then step by step expanding that right to one of staying there with the slaves indefinitely--and perhaps even buying and selling them. (The issue was often spoken of as the slaveholder's right of "transit or sojourn." "Transit" might seem to imply a short presence in the free states on the way to a slave state; but "sojourn" could mean virtually indefinite presence of slaveholders and their slaves in northern states, just as long as the slaveholders do not declare an intention to become permanent residents--remember that John Emerson with his slave Dred Scott had "sojourned" in Illinois and the Wisconsin Territory for years...)"
https://www.alternatehistory.com/fo...r-of-northern-secession.471503/#post-19648288
It would therefore technically be possible for free states to join the Confederacy (subject to "transit or sojourn" etc.). Indeed, some Confederate leaders did hope to lure nonslaveholding states into the Confederacy--to (in effect) make the Confederacy the "new" or "real" United States, with the "fanatical" New England states (and perhaps Upstate New York if New York City seceded from the state of New York) left out. Others however feared this would just mean re-creating the slavery issue on Confederate soil--and partly for that reason, it was made harder to admit states into the Confederacy than it had been to the United States. ("Other States may be admitted into this Confederacy by a vote of two-thirds of the whole House of Representatives and two-thirds of the Senate, the Senate voting by States...")