The verdict
If you run a services firm and need to know whether a project is on budget, who has capacity and which client makes money, pick Productive. If you sell software or products online and need a payment layer that works every time, pick Stripe.
An agency that also sells a product could reasonably use both, since one plans and tracks the work and the other takes the payments. I would not expect Stripe to tell you project profit, and I would not expect Productive to be a developer-friendly payments platform with webhooks and a CLI. Each is strong where the other is not meant to compete.