Stripe appears to be the leading competitor to Paypal. Their fees are lower (2.9% + 0.30) and they accept all major credit, debit, and pre-paid card. But more importantly they have a partnership with Apple Pay ( https://stripe.com/apple-pay ) which opens the door for more mobile users and they already have early talks with Samsung's LoopPay ( http://www.engadget.com/2015/02/18/samsung-buys-looppay/ ) regarding their Apple Pay competitor, and finally they also accept Bitcoin ( https://stripe.com/bitcoin ).
Stripe just became a contender against Paypal offering more payment options and better mobile support. They of course support both 1 time purchases and subscription payments.
My suggestion is NOT to replace the current paypal integration, but rather also include Stripe integration. They make it very easy to develop for. https://stripe.com/docs
As a added bonus, they have a better policy regarding digital products and subscriptions, offering better seller protection.