What makes fonts in Ubuntu as sharp as fonts optimized by ClearType on Windows?

Both systems, Microsoft's ClearType and FreeType, use Subpixel Rendering, which utilises the RGB subpixels on your TFT display to make the glyphs appear sharper and improve their form.

One important difference is that Windows tries much harder to fit the font into 'the pixel grid', which is why it looks 'sharper', at the expense of the glyphs' contours:

ClearType also uses very heavy font hinting to force the font to fit into the pixel grid. This increases edge contrast and readability of small fonts at the expense of font rendering fidelity and has been criticised by graphic designers for making different fonts look similar.
_{from Wikipedia's ClearType}

Posting this answer here so that I can find the answer next time when I search for "clear type ubuntu": (I hope this will help others too)
One approach is:

1. Install Unity Tweak Tool sudo apt-get install unity-tweak-tool
2. run unity-tweak-tool in terminal (this starts the GUI)

3. Go to Fonts

   

4. Under Appearance you will find Antialiasing (none/Grayscale/RGBA).

   

Another approach is:
1. Install dconf editor
2. Search for "antialiasing"
3. If you cannot find it, the setting is under:
org/gnome/settings-daemon/plugins/xsettings
And there you will find the antialiasing.