One way to fill a god’s enormous shoes is to get collagen injections in your feet. But that’s not covered by health insurance, even for top executives. That leaves two options–to promise to continue your predecessor’s long winning streak, or to establish several degrees of separation from the old boss and tell shareholders to reduce their expectations. Palmisano, who was anointed in January and took office in March, warned in April that IBM’s glory days were over. Separation City. IBM shares plunged a hairy 10 percent in a single day. But because Gerstner was still on the premises as non-executive chairman, that decline got posted to Big Lou’s account rather than to Palmisano’s; heck, even if he were working at Internet speed, Palmisano couldn’t possibly have messed up Big Blue so badly that quickly. That strategy worked, at least for now, because no one is demanding Palmisano’s head.

Then there’s Immelt. From the time he was anointed in November 2000 until taking over last Sept. 7, Immelt repeatedly said that the double-digit growth that GE posted under Welch could continue indefinitely. Granted, Immelt couldn’t possibly have known that Enron would implode, which would increase investor scrutiny of the kind of accounting games that companies like GE routinely played, such as taking profits on pension-fund surpluses. He couldn’t have known that the 9-11 attacks would traumatize the country. And he couldn’t have known that Welch would end up in a messy, public extramarital affair. Welch’s private life matters because having him turn into an object of ridicule dimmed the aura that surrounded GE during much of his reign. It’s hard to revere a man photographed driving his much younger paramour around. None of this is Immelt’s fault–but that’s life in the fast lane.

Both IBM and GE stocks have underperformed the market since their new chief executives took over. But Palmisano isn’t under attack. Immelt is, by people ranging from bond maven Bill Gross, who criticized GE’s lack of financial disclosure, to stockholders at last week’s annual meeting. GE stock is down 22 percent since the Immelt era began, while the benchmark Standard & Poor’s 500 Index is down only 1 percent. Had GE lost more than 20 points to the S&P during Welch’s regime, he probably would have committed ritual suicide in front of company headquarters. Unless you believe that Immelt has introduced a fast-acting financial poison into GE’s water supply, you can’t attribute this decline to anything he’s done or not done at the company. Immelt’s advocates point out that GE’s first-quarter profits met Wall Street’s expectations. But the stock price hasn’t–and the stock price is how CEOs are judged these days.

I would love to give you Immelt’s, Palmisano’s, Welch’s and Gerstner’s views of events. Alas, none of the four would talk to me. IBM and GE declined to comment. So I’m relying on my own analysis, supplemented with background interviews.

I think that part of the reason Palmisano and Immelt have taken different approaches to succeeding the boss has to do with personal relationships. I’d bet that Immelt, a GE lifer like Welch, venerates his former boss, while IBM lifer Palmisano is far more realistic about Gerstner. Gerstner, you may recall, parachuted into IBM a decade ago as its designated savior, and has done a great job of getting IBM’s stock price up. But there have been quibbles about IBM’s business performance–as opposed to its stock performance–for years. And Gerstner, for all his success, has a history of leaving financial messes behind at his last two pre-IBM jobs: RJR and American Express. These weren’t horrible problems–but they’re certainly enough to make any successor wary. Which Palmisano clearly was.

It may also be that Gerstner and Welch happened to reach retirement age at opportune moments. Look what’s become of once hot chief executives like Bernie Ebbers of WorldCom, Dennis Kosloski of Tyco and Mike Armstrong of AT&T. They used to be stock-market gods. Now they’ve been cast out of the pantheon. The only good news here is for their successors, for whom the bar will be set really low. Filling big shoes is a big problem. Filling shrunken shoes left by fallen gods is a heck of a lot easier.