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And the wealth management market is still growing apace, according to Scorpio. In local currencies, J.P. Morgan hiked its volume by more than 20 percent on the year, while Citigroup managed a 17 percent climb, and Morgan Stanley 14 percent growth.

At UBS, managed assets edged nearly 12 percent higher, while Credit Suisse's rose by more than 13 percent. Julius Baer, which thanks much of its heady recent growth to the 2012 acquisition of Merrill Lynch's international wealth arm, managed almost 15 percent.

U.S. Home Advantage

The American banks are also cementing strong positions in key global markets like Asia, where UBS and Credit Suisse share the podium with Citigroup. Morgan Stanley and Goldman Sachs – an investment banking powerhouse with an almost incidental wealth arm – is among the top-ten by assets.

In the U.S., still the world's most plentiful private banking market, the U.S. banks have a home-field advantage. There, J.P. Morgan leads, followed by Goldman Sachs, while Bofa's Merrill Lynch Wealth Management leads with the ultra-rich. 

UBS as David

U.S. private banks are also increasingly testing their European rivals on their home turf. Northern Trust, which is the second-largest family office in the world, has discovered Europe. In Switzerland, J.P. Morgan and Citigroup are distinctively pursuing a growth strategy.

The stealth advances by U.S. banks shed new light on UBS' decision earlier this year to fold its American ex-Paine Webber brokerage together with the wider ultra-rich unit. UBS boss Ermotti clearly views the Swiss giant in the role of David when he challenges his American counterparts for business with U.S. expat clients, as disclosed last month.