Given a long enough time span, slavery would have died naturally in both regions. Foreign cotton producers would have started to mechanize production and slavery would have been outcompeted. It would have died because it would no longer have been profitable.
In the shorter term, slavery would have died a natural death in the upper South before it died in the lower South. Very little cotton was grown in the upper South by the 1850s. The areas that had the highest concentrations of slaves were those cotton-producing areas in the lower South. Slavery was becoming less and less important to the economy of the upper South and would have died there much sooner than in the lower South.