Doing the drywall over the old ceiling works just remember all the light fixture boxes will need to be moved a bit and please do not do any kind of texture this time. The mess is still an issue with mudding and taping.

Are costs about the same either way (new drywall vs scraping popcorn)? Thanks much.

Before you do any more popcorn ceiling removal, what is the age of the ceilings? If they are older than about 1980, have they been tested for asbestos?

1980--That's about the exact vintage.

They quit using asbestos in ceilings in the late 1970's, but contractors were allowed to use up their existing stocks so it was still being done a couple of years later in some cases. You are on the borderline, so I suggest you have a certified asbestos test lab assay a sample. This is typically less than $100.