Stripe is a bit younger, except Pin (which was operating in Australa first though). Pin did mention somewhere that they had a very special partnership with one of the 4 pillar banks that would have been difficult to create.
Both Pin and Braintree go through NAB; they seem to be the only bank that's willing to deal with international payment gateways (not sure why exactly). I know you can go through their API directly, but I'm not sure anyone would want to.
Pin Payments is owned by the big four Australian banks. They have a vested interest to make sure it is harder for competitors to enter the market, not easier.