When people get banned from Paypal or they're looking for a new platform entirely because they want a change, they usually check out Stripe as one of their options. Stripe has been around for a while now and is rising popularity because they pride themselves on their security. There are advance fraud filters that you can adjust to block or accept payments from people who have less than credible purchasing histories.
Stripe is definitely powerful, but still has two downside of Stripe is that you can't use it for certain niches like direct marketing, which is what I going to use it for, because it goes against some terms they have in place. The other downside is that they only allow a few dozen countries to access them, which mean you cant accept a payment unless your buyers are from those specific areas, and that means lower sales for you if you sell internationally.