I want to update the URL using window.location.hash or history.pushState.
What are the differences and advantages of each method?
location.hash has a better support than the history.pushState method.
The advantage of the pushState method is that you can bind a state to the history entry.
If you don't need this state object, I recommend to use the location.hash property, to have better compatibility with older browsers.
location.hash = 'new-hash';
console.log(history.state); // null or undefined
history.pushState({extraData: "some state info"}, '', 'new-hash'); //<---
console.log(history.state); // [object Object] = {"extraData": "some state info"}