In order to make a right decision, you should compare pros and cons of both carts. Firstly, let's talk about PrestaShop.
Main benefits of Prestashop shopping cart are:
1. Intuitive admin panel. Platform is easy to use from backend and storefront. So, your customers will get a positive shopping experience.
2. Customizable. No limitations in quantity of products, users, orders. Over 310 default features.
3. SEO and Marketing tools. Marketing features like coupon codes, discounts, etc. Google analytics will help to track the results of promotion campaigns, conversion rate, sales, etc.
Cons: not stable after major upgrades, some important extensions are available only for additional costs.
Main advantages of WooCommerce:
1. Possibility to sell physical and digital products.
2. Additional opportunities, since WooCommerce is WordPress CMS plugin (possibility to set up a forum, blog)
3. Secure customer account, robust tax settings and options, discount coupons.
Drawbacks: lack of languages, currencies, shipping methods, inability to add product variants.
Its a really short comparison. I would advise you to find more detailed information in order to make a right decision.