PayPal is so universal, we considered using it. We decided against it for these reasons:

Privacy: PayPal allows us to see your name and address. In our experience, people don't like to share this information.

Terms: PayPal has you forever once they have you. There would be no way for us to move to another provider should their services no longer prove adequate.

History: PayPal has been known to treat their customers unfairly. Frozen funds, misidentified fraud and other reports of heavy-handed behavior gets covered in the press too often for our tastes.

Stripe appears to be doing their best to support their customers, both vendors and consumers. They're a PCI Service Provider Level 1  so they adhere to the strictest security measures possible.