I wouldn’t assume it’s exclusive. At the scale of Uber, it may be worth keeping both systems running and split usage between the two to negotiate the best rates.
However, if they're trying to do per ride auths, then they might need redundancy there. Hard to imagine they do that.
Ahh yeah, and also at the international scale. The article also states that Stripe is expanding internationally (Didi Chuxing, Grab), so it could be that Stripe handles Uber's international payments, whereas Braintree handles the U.S. ones.