Personally I reckon 1 the most natural.
Construct an edge grid, fill in the tile so it doesn't overlap its neigbours and that's what you get.
Personally I find the idea of engineering in unneeded overdraw highly offensive.
Being a bit of a perfectionist engineer, I myself has tried my hand at trying to find out if there is single "right one"... it's a very nice example with the grid you show there... however, if you approach the problem differently in that you consider a square, rotate it 45 degrees, and then shrink it to 50% on the height... then you end up with #2 instead (and possibly #4 depending on how you scale it... interestingly enough, you used #4 as an overlay in your second picture)!
But indeed, the fact that the outline in your example is a power of 2 128x64 ... is very nice indeed!
And I remember even trying to construct perfectly tiling ~45 degree and ~22.5 degree slopes with both #1 and #2 to see if any of them showed a more "mathematically" quality, but from what I remember, both could be constructed with a fixed line stepping pattern. However, #1 was slightly ahead in visual quality as all edges are 2px wide, meaning the slopes connected a bit more beautifully. (Found the old image!)
#1 is to the left and #2 is to the right.
In this example, I would say that #1 is slightly ahead of #2 in terms of visual quality, in #1 both slopes connect well to the center and also to each other, they're also a bit more evently sized in #1.
Oh and I definately agree about the overdraw, but when you're using an outline, it might make sense, as in that the outline of two adjacent objects would then merge instead of forming a thicker outline, but only diagonally ... which your picture actually illustrates beautifully ... perhaps that's the way to go! #1 really seems to be "mathematically" favored and you can't argue against math!
But I'm curious as to what the practical implications are for pixel art made using the various styles. E.g, using #4 has two center lines which may be very nice in a way, but makes diagonal grid lines impossible.
I think #2, with left-most pixel yellow. (Note to self: Have to sit down one day and hammer out all the logic behind isometrics & its transformations)
It's interesting from what I've seen on the internet in that it seems like neither of #1 or #2 is favored, both appear to be equally used, I've even seen a single pixel artist use both.
And from what I've seen when looking around it would seem like some prefer #2 as it has a softer feel to it, buildings and similar things don't get such prominently "angled" edges but rather gets a softer and flatter overall feeling. While #1 has really hard edges that really has a more 3D feeling to it. And #4 is kind of nice in that it does have center lines (vertically and horizontally), highly organic and non-regular tilesets seems to like use this one sometimes, but horrible if you want to draw a grid pattern.
What I mean is that, more realistically crafted pixel art seems to favor #2 to some degree while simpler and more abstract pixel art seems to favor #1 for having a bit more 3D to it and because the corners are all even in size.
