This report in Keywords Explorer shows the domains that get the most organic traffic based on the keywords and target country entered into Keywords Explorer:

You can use this to find new competitor websites. First, enter in a list of keywords, and select a country. You will get a list of domains that receive the most traffic from the keywords you entered in:

You can drill further to see how they rank for these pages by clicking on the caret next to a domain, and opening up their Organic keywords report or Top pages report, which can give more information about their SEO tactics:

The same can be done with the Traffic share by pages report:

This can be useful in finding content ideas for a group of keywords, based on what kind of pages rank for them.

Note: if you wish to find competitors for the keywords that your website already ranks for, you can use the Organic competitors report instead.