Cost will depend on how you go about the change. The cheapest change would be to scrape it all and the paint the smooth wall. Add some cost to scraping and then applying a different texture. Alternatively, you could just drywall over the existing g texture to start fresh. But, that’s both cost and labor intensive. Scraping only costs some sweat equity.
Scraping means to scrape it off so as to expose the drywall underneath. But, it will be much much harder if it’s already painted. Your contractor has the right idea. Skim coat it or put new drywall over it. Probably cheaper, too, if you’re paying for the labor.