The president is also losing the war of words because his Comey-related decisions have been tactically unwise.
The president's firing of Comey in May led to one highly capable and principled former FBI director being appointed special counsel and another having a score to settle and a record to set straight.
"A Higher Loyalty" and the accompanying media circus likely will not hurt the president's reputation much since it mostly goes over ground that has already been covered extensively.
But will it help or hurt Comey's reputation? The book's emphasis on the importance of values and ethical leadership may help reinforce his reputation as a person of integrity.
Still, Comey had a harder time in the Sunday evening interview than a person of courage and integrity should have when pressed to explain why he didn't stand up to the president when asked for a pledge of personal loyalty, or when asked to back off the Flynn investigation.
And his admission that political considerations may have played a part in his reopening of the Clinton email investigation in the crucial final days of the 2016 election campaign will lower whatever opinion many Republicans and Democrats already have of him in terms of both character and judgment.
His acknowledgment in the book that he "can be stubborn, prideful, overconfident, and driven by ego" won't help his reputation either.
Will the attention surrounding Comey's book hurt the Russia investigation itself? The probe began when Comey was FBI director, after all, and his recent public criticism of the president may raise the question whether the probe was motivated from the outset by personal bias.
I believe the Russia investigation is safe chiefly because of the unassailable integrity and tactical savvy of special counsel Robert Mueller. Both Trump and Comey would be wise to take a few pages from Mueller's playbook on silence, patience and humility.
Mueller has not spoken a word in public about the Russia investigation since being appointed in May despite attacks on the integrity of his team and probe. That feat of restraint seems beyond both Trump and Comey.
Comey's controversial public statements exposed the Clinton email investigation to bipartisan criticism, while Mueller's silence shields the Russia probe from similar criticism.
Comey has provided fuel for Trump's Twitter flamethrower, while Mueller has not.
In the commencement address he delivered at his granddaughter's graduation from Tabor Academy in May, Mueller described humility as "the idea that the world does not revolve around you." That idea would be a much-needed revelation to Trump and a helpful reminder to Comey.
In the same commencement address Mueller cited the author Barbara Johnson's definition of patience as "the ability to idle your motor when you feel like stripping your gears."
While the war of words between Trump and Comey sounds like the stripping of gears, the patience of Robert Mueller sounds like a powerful engine more than ready to do the important work it has to do.
Mueller clearly knows that he has more important things to do than engage in a public war of words. The president of the United States and his former FBI director should have more important things to do as well.
Commentary by Joseph Holt, a business ethics professor at the University of Notre Dame's Mendoza College of Business. Follow him on Twitter @busethicsdude.
For more insight from CNBC contributors, follow @CNBCopinion on Twitter.
