Braintree is owned by PayPal, so it is the one other payment service that can take PayPal. The appeal of Braintree is that it makes taking multiple forms of payments (e.g. credit cards and PayPal and Apple Pay, for example) much easier, and through just one set of APIs.
Think of Chargebee as your off-the-shelf, plug-and-play billing solution delivered on the cloud.
With Chargebee, you can set recurring billing frequencies and get paid automatically by your customers. You can easily combine recurring, one-time, and usage-based pricing models.
A "Revenue Management Framework" to help with payments and be flexible, like run pricing experiments, handle discounts, personalize offers, and provide insight along the way.
A no-code-required solution for accepting recurring payments for stuff like digital products, gym memberships, dog walkers, etc.
Something like PayPals very simple Buy Now buttons where you send users to PayPal's websites to buy things, and they are redirected back, are a good match for a static website.
Recurly is a SaaS-based company providing recurring billing management. Choose from multiple billing models, payment gateways, and payment options.
Probably the second most beloved payment service out there, with good clean APIs for dealing with payments, customers, and subscriptions.