I assume by "location in regard to another" you're not concerned about distance? Because 1-1-1 does not do relative distance between battlemat features (including PCs) well at all. And, as I indicated in the OP, not only is that important to me, but it's important under 4E's own rules. (You cannot trust actual distance on the battlemat in 4E the way you can in 3.5. When it has an effect on the rules -- and for a ranger, that's almost always -- you need to count and often recount.)
It also matters in cases, e.g., in which an encounter area includes rooms on the diagonal. There can easily be cases in 4E where an ostensibly 25' square room literally cannot fit where it should be able to fit, because it's drawn on the diagonal.
I also find it odd that whether or not a Burst 2 effect fills a 5x5 room depends on whether that room is drawn on the diagonal. If it's not, the burst reachs wall-to-wall. If it is, the burst covers exactly half the area. In other words, a 5x5 room in 4E that's drawn on the diagonal is literally twice as large on the battlemat as a 5x5 room that's drawn on the straights.
That freaks me out.
For distance measurements, I've adopted the same strategy other posters have advocated: quickly eyeball which is longer, X or Y axis, simply count that. Fast and easy.

As for your second point, I'm not sure I'm visualizing how the 1-1-1 rule of 4E is any way superior to the 1-2-1 of 3.x here. I mean, it seems to me the problem is rooted in the abstraction of the grid itself, not in how diagonals are measured. Wouldn't you also have discrepancies under 1-2-1? Could someone mock up a visual here for me?
(To whit: It seems a 5x5 room should have the same number of "squares" no matter what. The problem comes in when trying to use the same grid for two rooms that do not orient in the same manner; this is a failing of using the grid overlay to me. Unless I misunderstand the issue ...)