Google has made its feelings very clear: they like responsive design. The web giant has always been very vocal about user experience and content accessibility. Their mission statement, "to make the world’s information universally accessible and useful," doesn't mince words. They've identified responsive as the preferred approach to achieving this goal.
Google has access to a lot web data (obviously), and they’ve highlighted major increases in consumption across devices and screen sizes. They’ve been increasingly assertive about their preferences, writing in a post about smartphone-optimized websites they support:
"Sites that serve all devices on the same set of URLs, with each URL serving the same HTML to all devices and using just CSS to change how the page is rendered on the device. This is Google’s recommended configuration."
Google consistently identifies two advantages of responsive:
A Better User Experience
Google believes "using a single URL for a piece of content makes it easier for your users to interact with, share, and link to your content." Their algorithms notice decreased engagement with desktop sites on mobile, and increased load times with mobile redirects. People get frustrated by content that's not optimized, and shows in the data.
The bottom line for Google: they can more efficiently crawl and index responsive sites with one URL. But this is a positive for your site too. The easier it is for Google to understand your core content, the better for your SEO. Having one URL is great for your page authority -- sites with one URL for each page will attract more links to key pages.
Further proof of Google's preference can be found in it's own site creation. The Chromebook site -- among many other Google sites -- is responsive.
Google’s opinion is a powerful addition to the case for responsive design, and one that your clients will notice.