Responsive website are most preferable now a days. If a website is responsive with perfect SEO then there is no going back.
Google prefers Responsive sites as a solution for mobile friendly sites. If a site is not indexed by a search engine, then it will not have visibility when someone searches for it. This is often more problematic with mobile URLs.
For any site to be indexed, search engine need to crawl it and follow links to all the sites content and store the URL’s. In order to check the effectiveness of your site, you can run a site crawler like Screaming Fog or SEO crawler. This will allow you to check if there is any problem with your site. This must be cross checked with both BING and GOOGLE since both have developer tools that can check for any crawl errors.
Search Engine limit their crawl for each site, based on the site’s PAGERANK. If your site has more than one URL associated with it, then it would be more difficult, since the PAGERANK is divided between the URL’s.
Website owners communicate with crawlers via a SITEMAP. It is important to create a clear cut sitemap without any crawling errors.
Google Search Engine can read only text, and it cannot use anything which it cannot see.
Mobile users tend to spend much more time on social platforms than traditional PC users, so assisting mobile users with content sharing is a good idea. Google has witnessed mobile sites with video that is not playable so often, that it is considering penalizing sites with unplayable videos.
Google recommends the usage of HTML5 and avoid using FLASH, which is not supported by most mobile devices.
Responsive sites are often slow. This can have a harmful effect on SEO. Google penalizes sites that are slow loading. Google has provided developers with several resources to speed up their sites.
Google prefers sites at are user friendly and they don’t like to send visitors to sites which are not user friendly. Keep all this in mind while designing a Responsive Website.