MacBook – increase the resolution of a 13-inch MacBook Pro

Images and icons look about the same because of integral scaling. But text in non-Retina apps looks clearly worse. The difference is that on a non-Retina display, text uses sub-pixel rendering. But with Retina, old apps use full-pixel anti-aliasing instead. (Those full pixels are then multiplied perfectly with integral scaling.) Not quite sure what Retina text on a Retina display uses, it's hard to eyeball.

Separately, other resolutions look pretty good. The highest is 1920x1200. The trick is they are also rendered in double-resolution (3840x2400) and then scaled down for the display (2880x1800). Because there are so many tiny pixels, the result is acceptable, but the optimal setting is definitely sharper.

So Retina apps at 1920 look pretty good, and non-Retina text at 1920 has smaller and slightly fuzzier full-pixel anti-aliasing.

Every monitor does better in its native resolution (yours is 2560x1600). That's because the monitor always "adjusts" (scales the pixels) from the resolution you set to its "native".

For the best clarity you must set the resolution of your system to 2560x1600.