While there is no tool that will let you peek into the actual traffic stats of a particular website, you can use the circumstantial evidence to piece the overall popularity of pages together.
As mentioned by the previous posters, you can use buzzsumo to find a popular content on your competitors' websites.
Keep in mind that this popularity is measured primarily in terms of social media shares.
Just because something is popular in social media, it doesn't mean that it is pulling a lot of traffic.
People can share a lot of Facebook links but it doesn't mean that people are actually clicking on those links and consuming its contents.
By the same token, paying attention to the number of backlinks' particular pages, can be a measure of popularity, but we really can't be sure as to whether these links translate to flesh and blood human beings consuming that content.
It is best to pay attention to both measures and also, if your competitors are blog sites, look at the number of comments and other internal indicators of activity.
By paying attention to these three factors, you should get a rough idea of how popular a particular page is.