they do go ever so slightly thicker towards the bottom, but as Mr Wood said, the extra height of the tyre help prevent punctures too, but don't get me wrong, you need to be smooth otherwise you'll still get punctures.
My vote is for a Rain King, I have used them for over a year now and I am still to get a single puncture with one, plus they are the grippiest tyres for sale (FACT!) and they don't easily fold either which makes them the most predicable tyre on off-camber surfaces EVER!