Font anti-aliasing is done automatically in the browser when you don’t add any effects to it like a GlowFilter. When running AIR the font is not anti-aliased:

Verdana, Not embedded, Browser

Verdana, Not embedded, AIR

If you want to do effects like alpha and rotation on fonts, you have to embed them into your SWF. This also results in anti-aliasing when you run your application as AIR file:

Verdana, Embedded, Browser

Verdana, Embedded, AIR

Though the strange thing is the 0 (zero) and o (O) are missing a bit on the top right.