Hyper-Threading P4s became available in November of 02, though indeed the 800mhz FSB 'C' revision didn't release until April of '03.
The K8's initial release in September of '03 was problematic, for several reasons (at least on the desktop front, for workstations it was much less so).
It launched first with Socket 940, which demanded special ram, and the mainboards were quite expensive. The clawhammer 3200+ on socket 754 was a pretty even competitor for the P4 3.2, beating it in more than it lost imho, but we all know how socket 754 turned out.
In a weird way, Intel became the value leader during this time, as you could get a cheap Socket 478 setup, use dual-channel regular DDR, and overclock a cheap Northwood to ~3.2ghz or a little more, wheras the AMD64 chips and especially socket 940 mobos/ram, were quite expensive and uncommon.
Where AMD finally started getting good traction was in June of 2004, when they launched socket 939, eliminating the need for buffered DDR, and simultaneously launched Winchester. The doubling of memory performance, increase in HT from 800 to 1000, and overall affordability (it now made perfect sense for new buyers to grab a s939 board and a midrange A64 chip) made it begin it's march to total leadership. P4s were still competitive in performance, but this is where I think it was hands-down the better choice to go AMD64.
Things are a lot more complex than people commonly remember. K8 might have been released only 5 months after the P4C, and 10 months after the first hyper-threading P4s, but it was really about a year to a year and a half before AMD's really started going places with AMD64, eventually leaving P4 in the dust completely.