You can check to see if they are using Quantcast and have made their data public or are big enough to get an estimation: https://www.quantcast.com/newsvine.com
Here are some more tools for see how much daily visits my competitor website is getting. Compete, Google Ad Planner, Google Insights, Google Trends and SEMrush.
Hi Here are some good sources for answer to your question. Basically, run the same tools on YOUR website, to see how accurate each tool is, you'd know how right it is about your competitors. Also, what could you do after it, that is the big question. http://socialmedia.biz/2011/01/10/7-tools-to-monitor-your-competitors-traffic/ http://moz.com/blog/monitor-competitor-traffic