You don't choose between those two routers, they are not replacements for each other.
At the risk of stating the obvious, the Angular router handles routing for the Angular frontend, the Go router handles routing for the Go backend (the initial page load, the AJAX calls made from Angular to get data...).
We use angular as an MVW for front-end
We use django + django-rest-framework for back-end.
It's important to understand that "routing" in angular is a bit "synthetic" - it's not actually requesting much from the server after index.html loads (it only changes address etc as part of the routing). So the routing is totally separate on the front-end, assuming you are using a back-end to provide the data.