I am assuming similar resolutions here.
No, you were not.
You are not being fair here by considering the Surface Pro 3 at HiDPI 2x only. The SP3 has a 2160x1440 resolution, which is much higher than the 1366x768 resolution of the 11-inch Air.
As far as I know, the SP3 uses 1.5x scaling, meaning an effective resolution of 1440x960, which is higher than 1366x768 of the 11-inch Air in all respects. This 1440x960 is also a little more than the 1440x900 resolution of the 13-inch Air.
I said it was for comparison sake; it's necessary if you want to compare with other screens that are or would fit in a Mac (we aren't gonna do again the discussion, Apple likely will use a screen at 2x not 1.5x. I might happen to be proved wrong on that, who knows). Of course, you can through software exploit the pixels of the screen different ways, and yes by default the SP3 is at 1.5x.
And of course, if you add to the previous list a 12"@1440x960, I'll agree this could be seen as the most "productive" screen. But, then again, we're down talking about pixel density and comfort of utilization and at 144ppi (equivalent at 1x) we're starting to reach some limits I'd argue (everything almost even 7% smaller on screen than on a MBA11 screen, itself already quite dense): yes the highest pixel density at 216 ppi allow to maintain legibility at small sizes, but there is a limit at going too small or force the user to come closer to the screen (or have to display text larger but then losing the interest of the larger resolution for a larger estate). Microsoft using by default this screen as a 1440x960 screen would be equivalent to Apple making 1920x1200 the default on its rMBP15 (144 vs 147 ppi equivalents).
But all that is not related to the aspect ratio as you presented it first, it's the [software/logic] resolution that allows you to then say it's a more "productive" screen.
the screen in the SP3 is also larger than in the Air:
Yes, you're right 66.7 sq. in. vs 57.6 sq. in. if you talk about physical size (I meant surface in term of pixels as a unit, not physically, and still considering it at 1080x720).
much more vertical space and just a very small amount of less horizontal space.
Physically yes, but not at 2x, which was how was compared the two screens.
So, the SP3 screen is better for productivity than the screen in the 11-inch Air: larger, more vertical space, and higher resolution.
Used at 1440x960, yes definitely more space than on the native resolution of the MBA11, no debate. That's not what was in discussion. If you're able to cope with a small UI, you could then consider a 11.6"@1600x900 screen is at least as much "productive", although being 16:9. But that's not how I approached the comparison, you also have to keep the pixel density in a reasonable range for 1x usage.
The only way to compare any given [range of] size of screen at any aspect ratio would be at fixed pixel density equivalent ideally, and then you could say a 12" 3:2 screen offers of course a larger surface than a 16:9 11.6" screen (both physically and in term of resolution as we'd be at fixed pixel size).
