Each has their own plus and minuses -
1. Shopify requires a monthly payment and needs a Shopify developer who is capable enough to work with it. Woocommerce doesn't.
2. Shopify offers limited functionality - everything else is supported by third party plugins - a lot of them are unmaintained and/or require "complete access" to your store.
3. Woo comes with its own share of plugins, but, unlike shopify - most "WooCommerce plugins" are open source and a competent developer should be able to modify them to your requirement.
4. If you need a particular feature, it is easier to develop and deploy it on WooCommerce vs. Shopify.
5. WooCommerce needs to be hardened and kept updated. Shopify manages the security for you.
The reason you'll find most big brands using shopify is due to the Shopify partners tag. The bigger partners have enormous price tags that come attached to their work. But then these people are selling brand creatives and not websites.