Stripe is strong because of their security. It is difficult for the programmer to install it, and in my case was impossible since my hosting provider did not have up-to-date software that it requires. I had to use another program on top of it as the shopping cart instead of using Stripe's shopping cart. But Stripe integrates with everything if you can get it to install, and is stable.

The big reason to go with PayPal is the 6 months same as cash or multiple payments over weeks for your clients. Some clients need this and you will lose them without PayPal. PayPal may change their policies, so in my opinion, PayPal is not as stable as Stripe. Some clients refuse or can't use PayPal, where Stripe is available to everyone with a credit card.

In summary, I set up both for my clients. And I used Zoho for everything else - shopping cart, accounting, CRM, banking, etc. It integrates with both Stripe and PayPal and pretty much anything else you use.

Be sure to read the Terms of both Stripe and PayPal, and I think that will help you with your decision.