Security and PCI Compliance
Stripe is a payment processor that takes security seriously. At the core, it's a very stable and secure platform and intrinsically encourages good security. It does this by ensuring that credit card data entered into our app checkout is sent directly to Stripe. This is so important, as it ensures that you are automatically PCI compliant. Becoming and maintaining PCI compliance is an expensive process, and the penalties (both financial and reputational) for falling foul of this can have significant consequences.
Well documented and easy to use
When Stripe first launched to the public, the Stripe API was a difference maker. It's clean, well documented, and easy to implement. Payment processor APIs of the past were buggy, inconsistent, and poorly documented. In fact, PayPal was one of the worst offenders.
This is an area where other payment processors fall flat on their face. Imagine you've built a successful membership site over the years, and you powered it with PayPal subscriptions. If you want to move to another payment processor (like Stripe), you can't transfer that credit card data. PayPal simply won't give it you. All your existing customers would have to sign up again and you'd probably lose some of them during the process.
Stripe on the other hand values data portability. If you decide to leave Stripe they'll help you migrate your credit card data in a secure and PCI-Compliant way. This over accommodating stance on data portability is certainly worth noting. It's refreshing to know you have a choice, and won't be locked in forever.
Where other payment processors are suffering from scale, age, and bureaucracy; Stripe is new and hustling for market share. They're working hard to differentiate, and for now have chosen to use them as our payment processor.