@matigo Similar to cast iron — it seasons and retains heat. It absorbs the oils from previous brews, and enhances the flavour of succeeding brews, which is why you should have one pot for every style of tea (and obviously never brew anything with essential oil like Earl Grey in it). It also retains heat much better than a gaiwan because the clay's a lot thicker and heavier, which I find to be especially advantageous for pu-erh on the 10th brew. But the porosity also means that you can never wash them with detergent, and must take great care to keep them clean. Even letting mould grow can ruin the whole pot, as you might not be able to fully clean it.
They're also great as works of art, and the most expensive ones are…very expensive. So many different sizes and designs to choose from. Currently eyeing this one [yunnansourcing.com]
I won't get one for green or white tea, because they're not meant to be brewed at high temperatures anyway, and general practice for gongfu brewing is to use glazed gaiwans for them.
As for gaiwan advantages, the glazed ones don't season and so can be used for any tea (and as a drinking cup), and they pour incredibly quickly with practice (I can empty 150ml in about 2.5s). That makes them perfect for tasting notes where neutrality is important.