FRANKFURT (Reuters) - Deutsche Bank new chief executive faces the same strategic problem that has long preoccupied its top management - whether or not to override the rainmakers and big earners at its powerful investment bank to shrink that business.

Christian Sewing's appointment as chief executive on Sunday and the abrupt departure of his predecessor John Cryan holds out the prospect of radical change at Germany's flagship lender, which has been slower than rivals to reform after the financial crash.

Sewing expects to complete an initial review of Deutsche's investment bank within weeks, according to a person with knowledge of the matter, but any overhaul he launches is likely to take much longer.

"They've had to come around and painfully admit their investment banking baby is quite ugly," said Octavio Marenzi, CEO of consultancy Opimas. "That’s an emotional issue for them."

The debate over the investment bank's future heated up over the past two weeks as Deutsche Bank Chairman Paul Achleitner intensified a search for a CEO to replace Cryan, the Briton he had installed less than three years ago to clean up the bank.

Deutsche is already in the middle of a global review of the investment bank, known internally as Project Colombo, to determine the way forward as revenues shrink and clients and staff leave.

The appointment of Sewing - with a background in retail banking, auditing and risk - along with the resignation of one of Deutsche's top investment bankers, Marcus Schenck, suggests a shift away from the investment bank, analysts and investors say.

The 47-year-old CEO warned staff on Monday of tough decisions ahead. "The time pressure is on and the expectations are high from all sides," Sewing wrote in a letter to staff.

But it will be hard to reverse the investment bank's drive to compete with Wall Street that dates back to the 1990s. Employees say it resulted in the creation of fiefdoms and rivalries that proved difficult for any CEO to control.

The investment bank debate is tricky for Sewing because he is not an investment banker. He joined Deutsche out of school at age 19 at a branch in Bielefeld in north-west of Germany. He was crowned CEO in a hastily arranged board call late on Sunday.

The bank's major shareholders and top managers are also divided over how to proceed, with some favouring further investment in investment banking and others retrenchment.

Some analysts have said that even modest exits from specific business areas could erode revenues at the investment bank, which generates just over half the group's total.

The future of the investment bank is just one of many problems for Sewing, the third head of the bank in six years. He also has to tackle high costs, heavy losses and stiff competition in Germany's crowded banking market.

Peter Nerby, who analyses Deutsche for credit rating agency Moody's, pointed to tough competition among numerous international banks, asking "whether there's enough food for everyone".

That view was echoed elsewhere. Hendrik Leber, a fund manager with Acatis, said Deutsche should focus on German companies overseas: "Without the investment bank, Deutsche Bank would be much more reliable and profitable."

JPMorgan analysts said in a research note that Deutsche Bank should shrink its U.S. investment banking business to create shareholder value.

Schenck, the investment bank co-head, had wanted to expand it, but Achleitner, in an interview with the the Frankfurter Allgemeine Zeitung on Monday said: "The bank didn't currently support that effort."

Sewing has hinted he is open to a smaller investment bank in his staff memo on Monday, saying "we'll have to further adapt our revenue, cost and capital structure".

Some in Germany would welcome a return to Deutche Bank's roots - it was founded during the Industrial Revolution to finance German firms' expansion overseas.

"He has a huge task ahead of him that has big significance for Germany and our export orientated industry," Carsten Schneider, a prominent lawmaker from Germany's governing Social Democrats, told Reuters.

(Reporting by Tom Sims; Additional reporting by Arno Schuetze and Matthias Sobolewski; Editing by John O'Donnell and Jane Merriman)

By Tom Sims