Why fonts on Mac OS X look much nicer than on Windows when using the same hardware?

The software that performs the magic is called the font renderer. On a Mac, it's part of the Quartz engine. On Windows, it's called ClearType. You'll also notice that color representation is a bit better in OS X too.

In Windows, ClearType is optimized for on-screen readability. Apple optimizes their rendering for WYSIWYG (what you see is what you get) when printing. You can see this with bold and italicized text. The difference between bold and non-bold text is more subtle on a Mac whereas on Windows it's much more obvious -- especially at smaller point sizes. Apple also gets to cheat a little, because 90+% of Macs are attached to an Apple screen and they can cherry-pick what looks best on their own hardware, whereas Windows has to contend with some crappy low-res, no-name screens out there.

You can Google "OS X font rendering" to see that some people hate the way Apple renders fonts (usually from programmers and web designers), and others (like graphic artists and print shops) that love it. Either way, Apple is very proud of their font rendering, even going so far as to override ClearType in their Windows-based apps (Safari, iTunes, and QuickTime). This is part of where Apple's reputation for being "better" for graphics artists comes from.

99% of computer users don't think or care about stuff like font rendering, kerning, and color matching. But Apple puts in a lot of effort to specifically cater to that 1% of users that do.