The verdict
If you already run WordPress and want the shop inside the site, pick WooCommerce. It suits content-heavy stores and unusual products, and you keep control of hosting, data and payments. If nobody wants to maintain the store, or you sell to businesses and want B2B features, pick BigCommerce.
The cost comparison is not core against plan. WooCommerce is free to start but you pay for hosting, extensions, payment processing and developer time. BigCommerce charges for the plan, and the payment provider you pick changes the fees. Tally both honestly before you decide. For a small team without a developer, I would pick the hosted platform. For a team with WordPress and a trusted agency, WooCommerce makes more sense.