For that kind of information you may want to do some data-mining that would involve use of latent semantics and trend-watching... Or hire someone to do it for you - companies like Autonomy, NetSeer do such things.
Use this tool http://sharetally.co to check the total number of social media likes and shares received by any webpage. So if you want to know the most popular content of your competitor then you should look for most shared content on social media.
It also means you need to check each page manually, which will consume lots of time.
Interactive Bees, One of the Best Seo companies in India and it is well known as Social media marketing company in India.