I researched both extensively last year when looking to buy. The E46 M3 is superior to the 330i/Ci ZHP in just about every performance category aside from the steering and gearbox. It is faster, much more powerful, handles better at the limit due to the LSD (although at ~50% or less the ZHP is pretty much equal handling-wise), has better brakes and much beefier suspension.
The M3 is also significantly more expensive than the ZHP to maintain if you stick to "old school" BMW maintenance plans (PM on cooling system, Vanos, brakes, suspension, fluids/filters, bushings, etc.). Plus it has extra stuff to tend to like the LSD and valve adjustments.
One thing that really sold me on the ZHP, aside from cost to own and maintain, was the uniqueness, the subtleness and exclusivity. An M3 is quickly and easily identifiable; there is no mistaking it. The bulged wheel wheel arches, the quad exhaust, the badging...you stick out like a sore thumb. I realize a lot of people absolutely love this aspect of M3 ownership, but I like the subtle qualities the ZHP has. Further, there are almost 50k E46 M3s in North America, but not even 7k ZHPs. And the majority of those are sedans, not coupes. The ZHP also has unique bits like the Alcantara interior and M-Tech2 body kit.
I do wish I had that extra top-end power and LSD, but for a DD i don't really think I'm missing it all that much. I will probably try to find a nice ZCP M3 in a couple years once the miles start to rack up on my ZHP. For now I'm thoroughly happy with what I got.