Listify is powered by WooCommerce to process payments for listing packages, shop products, bookings etc. In fact all payment gateways that WooCommerce supports are compatible. This includes PayPal, Skrill, Authorize.net, Stripe etc.
Most directory themes only offer a few options in terms of payment gateways, but with Listify you can use any payment gateway that WooCommerce supports. This is over 116+ payment gateways. More information can be found here.