The different browser approach has the added benefit of letting you bind that app to a different desktop. The Chrome multi users can't be bound to different desktops automatically.

Also, I've found Chrome's multi user windows have a nasty tendency to fail to reopen all windows and all tabs upon reboot. One or two will open, but at least one won't, and when you do launch a new window for that user, it won't remember its prior tabs.

Your approach resolves both those cases. That said, Chrome's built in support with the prominent user icon in the window title bar is fantastic for multiple email accounts and the like, especially coupled with tab pinning so it can't help but open Gmail for example.

I was doing the same thing but got frustrated with things that would/wouldn't work in one browser but would in the other due to rendering engine differences and also not having certain extensions in one browser I had in the other. With multiple profiles in a single browser things stay consistent.