The real question would be WooCommerce or Shopify. WooCommerce is the defacto way to sell on WordPress sites. It was built to allow WordPress bloggers to monetize their sites and so if you have a WordPress site, WooCommerce is the way to go! Other benefits of WooCommerce are:
1. It is opensource and inexpensive. It is not free because you will likely need various third party plugins which cost money
2. It is simple to use and to get started.
3. Extremely flexible.
The drawbacks are:
1. It can be slow and if not implemented correctly, a performance nightmare.
2. You have to manage hiring developers to do extra work for you whereas Shopify "just works" out of the box.
The main issues with Shopify are the cost and lack of flexibility. For example, you can't really modify the checkout page even if you know for sure that adding certain elements will increase conversions.
But the great thing about Shopify is it "just works" and is highly optimized for most store owners.