Hard to say. At the time of writing this answer, Ripple (payment network) has about 200 or so banks signed up. A pretty small number, but much more than any other alternative provider out there, that just got started in the last few years.
With over 15,000 banks microfinance banks, credits unions, community banks, etc., some put this number as high as 25,000, the number signed up by Ripple is small. But then again, Ripple is just starting out.
Do not assume that just because Ripple has signed up a bank, that cross-border payment using Ripple’s technology becomes the default standard. It does not.
Society for Worldwide Interbank Financial Telecommunication (SWIFT) has introduced GPI (Global Payments Innovation) which was literally the laughing stock of the payments and banking in industry, when they claimed to have an edge over Ripple, by saying they would use the blockchain and settled in under 24-hours! (versus instantly by Ripple).
Today, SWIFT has realized, Ripple, et. al. represent a serious threat, and it (SWIFT) is doing all it can to convince banks to stay with SWIFT in the long run as SWIFT is working on more innovative solutions (which are yet to be seen).
Ripple’s ILP (Inter-Ledger Protocol) is extremely important. It could very well be the glue that binds the various payment atoms together to form the molecule known as frictionless payments.
However, I personally feel, politics will come into play. The Russians, Chinese, Indians, and a few other nations will be skeptical of one company’s technology stack becoming dominant in payments. Look what happens to Iran with SWIFT everytime sanctions are invoked.
Ripply, in my opinion, will be a player in the space, but I think the days of domination are over. There will be a multi-protocol payment stack that will include Ripple as part of the solution offering. Unless a global, open, equally contributed, XRP neutral standard comes out, no one company will dominate the space.