Increasingly, the world's biggest money managers are split over how much further inflation will retreat from the highest levels in decades. It's a debate that matters more than ever before, as bond traders ponder the end of the Federal Reserve's aggressive campaign of interest-rate hikes and wager on cuts starting within months.

On one side are firms such as Allianz Global Investors and TCW Group Inc., which say the Fed and other central banks will prevail with their rate hikes, even if it means up-ending their economies. On the other side are the likes of BlackRock Inc. and DoubleLine Group LP, which question whether policymakers are willing to throw millions out of work, or say inflation will remain elevated longer than many expect. That means it's too soon to bet on rate reductions.

The divide between investors with trillions at stake reflects just how tough monetary policy itself has become, particularly as price pressures—from the U.S. to the UK and the Eurozone—remain stubbornly high, and with readings of headline and underlying inflation sending mixed signals. Getting the call right could offer the surest shot at redemption after a punishing year for both bonds and stocks. It's a challenge that's put not only the largest firms in finance at odds, but those who work inside them, too.