Jes Staley runs one of the last full-service banks left in Europe that compete with Wall Street. The way the 62-year-old American banker sees it, his restructuring of UK-based Barclays has primed it to take on the likes of Goldman Sachs and Morgan Stanley.

British-born investor Edward Bramson couldn’t agree less, and his New York firm has bought a sizable stake in Barclays. He is trying to force the bank to scale back its Wall Street ambitions, to become a consumer and commercial lender with smaller investment-banking operations.