Done it on mine, and looked at doing it on mum's, so here's the answer:
3dr: Easy. As the new badge has lugs that go into the metal (which has rubber bushes, same method as BMW), you need to chop them off and file down the edges. I did try sticking it with double sided number plate pads at first, but it wouldn't sit down, so my bro used a bonding sealent (to quote Ben_R

), and after a couple of days it's rock solid and set down properly. Just make sure it's centred correctly, and that it is not on a rotated angle (my first attempt had FIAT sloping downwards!)
5dr: Not possible as where the badge goes, the boot has a contour line, so it won't sit down correctly. On the MY04>, the metal is pushed out to form a flat surface for the badge to sit on.
Then, the only difference is that "Stilo" now appears on the left; I left it on the right so it reads "FIAT Stilo" not "Stilo FIAT". The Abarth badge, and one assumes "16V/JTD", remains on the right.
The FIAT part number for the correct badge is: 51735551, around the £15 mark from what memory serves.