The original mandate of the Constitutional Convention was merely to amend the AoC. In a sense, the Constitutional Convention was a runaway convention in that it greatly exceeded its original authority when it scrapped the idea of amending the AoC and decided to draft an entirely new Constitution.
The runaway convention experience of 1787 concerns defenders of the U.S. Constitution today. If a convention to amend the AoC could end up scrapping and replacing the AoC, then a similar modern-day Constitutional Convention with the limited authority to amend the U.S. Constitution could end up scrapping the U.S. Constitution.
I think the difference is the AoC allowed congress to amend but the constitution requires amendments to be ratified by the states.