The latest issue of Bloomberg Businessweek gently chides President Obama for his recent comparison of the top two candidates to succeed Ben Bernanke as head of the Federal Reserve.

President Obama appears to think the two leading candidates to chair the Federal Reserve agree on monetary policy. On July 31 he told a group of Democratic senators that “when it comes down to their basic philosophy on the future of the Fed,” the differences between the candidates were so small “you couldn’t slide a paper between them,” according to Senator Dick Durbin of Illinois, who was at the meeting.

Obama might want to take a closer look at the candidates’ records. The fact is, you could slide a fairly thick doctoral thesis between the policy views of Larry Summers and Janet Yellen. In a nutshell, Summers is more skeptical than Yellen about the ability of easy money to accelerate economic growth; he also says the economy is closer to operating at full capacity than Yellen does. A Summers Fed would probably raise interest rates sooner than a Yellen Fed would.

Most of the commentary about the race to succeed Ben Bernanke next February has focused on gender, personality, and regulatory philosophy. All entertaining and important, but setting monetary policy will be the next chairman’s most important job. If Obama picks Yellen he’ll be casting his lot with faster growth and more jobs at the possible cost of higher inflation and asset bubbles. Choosing Summers is a vote for a more cautious approach—at the risk of higher unemployment.

Given the Federal Reserve‘s ability to generate wide-ranging economic mischief, it might be nice if the president spent some time studying this issue.