The higher res you go, the less differences there'll be between the two rendering methods. Fitting to the pixel-grid doesn't alter very much if the pixel grid is small enough.
Consider: Rendering a small font size at high-res is equivalent to rendering a larger font size at lower-res. If you look at the larger fonts on TFA's screenshot, e.g. "Node JS Design Patterns 101", there's proportionally much less difference (between Ubuntu and OSX) than at small sizes.
[There are even intermediate settings...]
[I don't agree with all their choices of what to call an "advanced" setting, but I think it's appropriate classification in this case.]
Seriously, you have to pick one: you either deform letter shapes so that they fit the grid better, with the disadvantage that your line breaks change and/or your letter and/or word spacing look awful, or you ignore the grid until the last moment, compute what percentage of each pixel is covered by each 'infinite resolution' graphene, and color them gray accordingly, with the disadvantage that text looks a bit more blurry.
(technically, there is a third way: layout each character of each font at some set of fixed point sizes by hand, so that it fits the grid perfectly. The original Mac used that method; it became infeasible when the LaserWriter shipped)
Edit: sorry, forgot the link, it's here: http://www.codinghorror.com/blog/2007/06/font-rendering-resp...
It's unlikely to be 'fixed' as it's a different philosophy between the OSs.
Mac renders fonts optimized for "correctness", which can appear fuzzy at low resolution. Their new hi-res (~200dpi) screens solve the problem, you get correctness and legibility.
Windows and Linux tend to optimize for screen legibility at low resolution, resulting in increased sharpness. At hi-res, they'll likely not look as correct as the Mac rendering.