It seems that both Adyen and Brainsomething processed over 50B last year whereas Stripe didn't.
Stripe didn't publish numbers (I'd dare saying because they are very small and that would scare big companies away), but the valuation at 5 Billion dollars indicates that they are less than 1/10th of the aforementioned providers.
Conclusion: Stripe = The hype underdog with strong marketing :D
Not at all. It only depends on your definition of big volume.
Source: By some metrics my company is > 1% of Adyen... or Stripe... or whatever competitor we decide to use at the moment.
If a single company can be as much as 1% of an entire payment provider, they gotta be quite small, right? Well, that's what I think every day when I see news about them :D
