Woocommerce is more complicated and has more moving parts. You’ll probably need more help from the programmer and have to get plugins (extra programs that work with your site) to get everything working. However, as Woocommerce is open source, the basic functionality is free and you will always have control of your site.
Shopify is a closed system that you pay on a monthly basis, and they also take a cut of your sales. However, things work more smoothly and you’ll probably have less problems overall, although with less flexibility. Finally, you will be at the mercy of Shopify, the company, in case they decide to raise their prices or do something else that will make it hard for you to run your shop.