Question about using credit card on WooCommerce

Okay, Im not sure if this is the right place, but I don’t really know where else to ask. I have a question about using WooCommerce. I have exclusively been only accepting payments through PayPal because I always thought that it was much safer than credit card. Problem is: not everyone has a PayPal account so I have to put a link to show my customers how to create one. But lately, I have been having problems with “Unverified” payments, since I guess not everyone knows that you need to verify your PayPal account after creating one. So I usually end up contacting the buyer trying to give them instructions on how to verify and they get all confused. So now I’m considering accepting credit card payments on my website as wll. My question (or rather my concern) is, how safe is the WooCommerce/eCommerce credit card payment gateway? Is it just as safe as PayPal?

https://www.ads-software.com/plugins/woocommerce/