PayPal and Stripe are both extremely well matched. Depending on your needs, you may be better off with either option. People tend to trust PayPal more, however, because it's been around for longer. So some customers may be hesitant to set up a Stripe account. That being said many people have been stung using PayPal, so the same logic could be applied to choosing its eCommerce platform over PayPal. They offer all the same core features needed to offer robust payment gateway functionality, so you'll need to look deeper into both platforms to find which one suits you best.