The verdict
If selling products is the business, pick Shopify. Checkout, payment handling, stock and orders all work together from day one, and its app and developer ecosystem is large.
If you run a company that sells services, software or consulting and needs a sharp marketing site, pick Framer. You can change a headline, build a campaign page and publish the same day.
Some teams use both: the marketing site on Framer and the shop on Shopify. That can look better than a store theme, but it means two systems to keep in step on branding, analytics and links. Only do it if the brand site really matters.
I'd not try to run a shop on Framer. I'd also not buy Shopify just to host a company website.