I'm well aware of Moom, BetterTouchTool, BetterSnapTool, Divvy, and Spectacle, and have thoroughly read this question's answers.
I don't think any of the above can:
with one keyboard stroke, tile the current window and the previously-focused window side-by-side.
Moom allows application-specific configurations; all the others allow manipulating only the current-focused window.
This is something I find that I'm doing over and over again, for example: switching from a PDF to my browser to type some info from the PDF into my browser; I'd like to quickly show them side-by-side so that it's easy to copy over, say, an address.