Right now, the new Microsoft Edge (Chromium) uses less RAM than Google Chrome. However, at the time of this writing (during the browser isn’t even have a beta version), asking a the memory usage of Edge is an unfair question, because the the browser is still under development and many of the features are not enabled.
As a result, the memory will be less and the browser can even be faster than Chrome.
Here’s a screenshot of the new Microsoft Edge vs Chrome RAM usage on Task Manager. As you can see, Chrome has 48 processes while Microsoft Edge has 39 processes, but both browsers have the same 6 tabs open.