It's not a matter of contesting the race to thinness. Here, the stuff is as thick as two not-especially-thin phones; it is reaching the realm of PDAs, except it hasn't got the clamshell and the keyboard.
It is pretty thick, but both my previous phones - Nokia N900 and Openmoko Neo Freerunner - were thicker. Personally the thickness doesn't bother me at all, it feels right in the hand; if I could magically change it without influencing anything else I would rather make the screen smaller.