The verdict
If you need a landing page, a waiting list or a quick offer test, pick Carrd. Nothing here needs a store, and Carrd is built for that speed.
If you sell products and WordPress is already your site, pick WooCommerce. The shop lives inside the site you have, and you control every part of it. It works best when you have a developer or a trusted agency.
If you sell products, have no WordPress and nobody to maintain a store, neither of these is the obvious answer. A hosted shop platform such as Shopify takes maintenance off you.
Because they do such different jobs, they can sit side by side. A Carrd page can run a campaign and point people to a WooCommerce shop that does the actual selling.