As you know, the onBlur event fires for an element if that element had the focus, but loses it.
The onFocusOut event fires in this case, but also triggers if any child element loses focus.
For example, you have a div with special formatting because the human is currently editing a field in that area. You'd could use onFocusOut to turn that formatting off when focus leaves that div.
Up until very recently, onFocusOut was only used by IE. If that has changed, it has been very recent. Test in FF, Chrome, etc.
The Jquery documentation has a good focusout vs. blur demo which I'll reproduce below for clarity. In short, focusout fires if the selector — $('p') in the demo — is anything including the inputs and parent elements. Whereas, blur only fires if the selector is on the inputs — $('input').
Few web developers consciously use event capturing or bubbling. In Web pages as they are made today, it is simply not necessary to let a bubbling event be handled by several different event handlers. Users might get confused by several things happening after one mouse click, and usually you want to keep your event handling scripts separated.