Despite their distinct histories and their storied rivalry, Apple and Microsoft have a lot in common these days. Both have shaped, in their own ways, personal computing as we know it today. Both see their futures in a mix of operating software, device manufacturing, and cloud-based services.

Both have unveiled new products this year to positive, if underwhelming, responses. Both have seen their stocks slump in the past couple of months, despite those new products and despite low price-earnings ratios (12 for Apple, 15 for Microsoft – Yes, Apple is now cheaper than Microsoft).

And now both have undergone management shakeups that look remarkably similar in many ways. This week, Microsoft announced that Steven Sinofsky, the man in charge of its most important operating software, was leaving the company to be replaced by other longtime executives. Although he had spent most of his career at Microsoft and was considered by many to be brilliant, he was also described as divisive, polarizing, and not playing well with other executives.

Swap out “Microsoft” for “Apple” and “Steven Sinofsky” for “Scott Forstall,” Apple’s now former VP of iOS, and you have a paragraph that also describes what happened at Apple only two weeks earlier.

It would be easy to overstate the similarities between Microsoft and Apple, and also between Sinofsky’s and Forstall’s departures. But some of the parallels are particularly telling. In the wake of both departures, former colleagues stepped forth to explain what happened, usually anonymously. The narrative emerging from Microsoft is that the company’s future will be more harmonious without him. Similarly, Apple’s future vision was said to be more seamless without Forstall.

On the surface, this sounds like two happy endings in the making for a pair of companies that were once the bitterest of enemies. But I suspect it will lead to something else: Several years of growing profits for both Microsoft and Apple, but years that are also more predictable, less inspired, and nowhere near as adventurous as they were under the influence of the brilliant but polarizing executives.

Apple has often been called the world’s largest startup, with some justification. It’s much harder to argue that Microsoft operates like a startup, but Sinofsky’s blunt, uncompromising managerial style helped Microsoft not only recover from Windows Vista with a more functional Windows 7, but also remake the operating software all over again with Windows 8.

And like Forstall, Sinofsky alienated a lot of people in the process. Which is often what it takes for a startup CEO to build a successful company. Innovation isn’t simply a matter of coming up with a bright new idea, it’s also the execution of that idea into the marketplace. The gap between the two swallows up a lot of talented startups. Making the leap requires a managerial will strong enough to make the decisions, compromises, and gut calls that are often so counterintuitive they seem crazy.

This is a big reason why life at startups is often so chaotic. Creativity among groups is rarely effective when it’s not messy. The group consensus of brainstorming can be comforting, but brainstorming is getting a bad rap these days, with evidence that dissent, conflict, or even solitude are more conducive to creativity.

A more harmonious corporate culture may be what Microsoft needs to execute a broad vision that links PCs, tablets, smartphones, the Xbox, and cloud services. Just as a more unified design and product vision may be what Apple needs to stay more focused and agile in a competitive industry. And so the executive shakeups at both companies are likely to bring some benefits.

But those benefits may come at the cost of losing the people who served as divisive but effective creators of operating systems. In today’s tech industry, operating software plays an enormous role in determining winners and losers. Sinofsky and Forstall stepped on a lot of toes to bring their visions of what an OS should be to the market. Neither will be a polarizing force at their old companies. But both Apple and Microsoft may be that much less bold in their thinking.

As they grow, Microsoft and Apple are heading into a safer, more harmonious future (Apple has been moving away from risk-taking for some time). And Forstall and Sinofsky are left to start over. Some people on Twitter, jokingly or not, suggested they should form their own company. If these two people famous for not playing well with others could somehow get along, they’d at least be at a company that understands what most startups know too well: Being innovative often means learning to live with messiness.