SAN FRANCISCO — If the Hatfields and McCoys lived in Silicon Valley, they’d be fighting with piles of cash and lines of software code instead of knives and shotguns. And the fight would be over who wins the most customers in the computer industry’s growing “cloud” of software services.

That’s how it is for Aneel Bhusri and Zachary Nelson, whose companies are in contention over the next major shift in computing. In a way, the men are reliving history.

Two decades ago, their mentors feuded, and that time, too, the dispute took place against the backdrop of a major shift in corporate computing — when customers gave up their mainframes and moved to software that relied on personal computers closely connected to a server.

Mr. Nelson, the chief executive of NetSuite, used to work for Lawrence J. Ellison, the billionaire chief executive of Oracle.