If screen real estate = supreme overlord then you want a Note.
The Note 3 won't be very long coming and will no doubt be quite fabulous. The Note 2 certainly is.
As for the nav bar on a 4.7" screen detracting from supreme overlord status, there are a lot of really happy Galaxy Nexus and Nexus 4 owners who would argue with you on that.
But if that's your criteria, fine, even without the nav bar, the SGS4 screen is larger.
And that will be sufficient cause for many. Sounds fair enough to me.
I was going to go spend some time with one today if time allowed. "Honey, I'm out the door, I have to go see the supreme overlord!" I don't think so.
PS - the nav bar on the One pops up as needed and goes away when not needed. And may go away on an update from HTC, just as it did last year. It's already gone away for most people rooting it.
Question - if I remove the nav bar from the One, does the SGS4 stay supreme overlord or will it just be the supreme lord at that point?