REDMOND, Wash.—Microsoft Corp. employees are passionate users of the latest tech toys. But there is one gadget love that many at the company dare not name: the iPhone.

The iPhone is made, of course, by Microsoft's longtime rival, Apple Inc. The device's success is a nagging reminder for Microsoft executives of how the company's own efforts to compete in the mobile business have fallen short in recent years. What is especially painful is that many of Microsoft's own employees are nuts for the device.

The...