Chrome

Console > Create Live Expression

document.activeElement

Click outside of the Live Expression UI to save

Hover over the result to highlight the focused element in the viewport. Right-click the result and select Reveal in Elements panel to show the element in the DOM Tree on the Elements panel. Right-click the result and select Store as global variable to create a variable reference to the node that you can use in the Console.

Firefox:

var lastElement = document.activeElement;
setInterval(function() {
  if (lastElement != document.activeElement) {
    lastElement = document.activeElement;
    console.log(document.activeElement);
  }
}, 100);