Either is safe, but I personally thing (and this is my personal opinion), Microsoft Edge values your privacy more. Chrome for a Google is a means to an end and its serving ads even when you can't see it. But where Chrome has the edge (no pun), is its greater support among the billions of web pages and extensions available.
Out of those two though, my default browser is Firefox, I think it beats the pants of both when it comes to privacy, security and performance. Also, the bookmark syncing is really reliable.