FORTUNE – In the web industry, imitation is much more than a sincere form of flattery. It’s an admission of another’s success, and an effort to catch up to the industry leader in hopes of surpassing them.

In social media, Facebook has been the leader everyone imitates for several years. Google (GOOG) tried a few times and came up short. But this month, that changed: Google+ is a formidable social media platform that matches Facebook in many ways and surpasses it in others, like realtime group video chat. Facebook quickly responded with its own video chat service, but couldn’t match Google’s. This back and forth is likely to continue for some time.

A decade ago, Google and Yahoo (YHOO) entered into a similarly intense competition over search. Google eventually won, of course, but anyone using search engines since then has also benefited because that competition advanced search technology very quickly. Web users may benefit from a Facebook-Google rivalry, but for a different reason: The best way for these companies to differentiate their social media offerings is by preserving personal privacy.

In other words, if things really heat up between Facebook and Google, privacy could become a real priority on social networks. Any technological innovation that one company produces can be copied quickly by the other.

Google and Facebook have been copying each other’s innovations for some time. First Facebook transforms from a simple web site to a web “platform” embracing thousands of other sites, then Google begins plotting a social “layer” over its core services. First Google hints that a social network should be broken up into multiple networks, then Facebook introduces this very feature with “Groups.” And now that Google+ features Hangouts’ video chat, Facebook has Skype-driven chat.

This cycle of innovate-then-imitate means neither company can hold the technological edge for long. Where there is likely to be a bigger gap is in privacy. Both companies have had major privacy snafus. Google Buzz flopped after its privacy defaults garnered bad press, and other privacy issues have drawn regulators’ scrutiny. Facebook has a long history of privacy concerns of its own.

Yet there are important differences in the two companies’ approaches to privacy. Mark Zuckerberg seems to be betting people will grow more comfortable sharing personal data with people and, more importantly, advertisers. “People have really gotten comfortable not only sharing more information and different kinds, but more openly and with more people,” he said last year to some controversy. Facebook has unabashedly designed its site to entice people into sharing more openly. As a result, it’s drawn much more ad revenue than, say, Twitter.

Google’s privacy mishaps has left it with a relatively conservative approach. That’s not to say it’s a model of privacy protection. The company still wants users to share data for more personalized search results, but it’s much easier to manage Google’s privacy options than Facebook’s. Reviews of Google+ mention its superior ability to manage personal data, better transparency on how that data is shared and the option to delete all your data. In fact, one of the more notable things about the launch of Google+ is that privacy was barely mentioned. There were a few bugs spotted and fixed, but nothing on the scale of the Buzz fiasco.

The question facing Google+ is whether the positive reception that beta users are having over the social service will cross over to a mainstream audience already familiar with Facebook. If better privacy is in fact a big factor for many people, then Google+ could easily become so popular enough that Facebook will be forced to improve its own privacy policies.

But if Zuckerberg is right that most people have simply grown cavalier about what they share about themselves online, then it may maintain its role at the center of the social media industry.