You can set up automatic payments which charges your card via the website on a specific date (weekly, monthly, yearly). I have been playing around with it over the last few days and it is the service Paypal wishes it was.naqua is obviously small fry in the scheme of things, but I use Paypal for 99% of transactions and have not had a dispute as yet. So from a business perspective, for me it works fine.
Stripe looks decent - but do you need to enter your CC details for every purchased, or do you have a profile like you do for Paypal? On the consumer side, the ease of Paypal and not having to dig my card out makes it attractive.