Not sure how to articulate the importance of the difference, but I was surprised to discover just how much I used and liked using the split view approach in Arc Browser, which is where I first saw it. It's the one thing that reliably makes me happy to switch back to Arc. (Its also prettier but that is very low on my priority list right now π )
Part of it is the ability to mix and match layouts within the browser environment. If I want to have multiple windows in Stage Manager to accomplish the same layout, it takes more effort to set up and adds overhead when switching (I need to switch multiple window focus's when changing apps), and it just generally doesn't work as well.