I’m using Firefox. I’m not sure of my preference, haha. With the separate window it can be standalone, like you said, especially if you like to resize windows and place them next to each other. On the other hand, if it’s just another tab and you already have the browser open then it’s easy to go between tabs that you could have something else on, such as documentation.
I think it would be great to have a configurable option to suit multiple styles.