Ignorance rears its ugly head:
It's not a choice between oil that has zddp or doesn't have zddp. It's a choice of how much zddp is in the oil. I am not aware of a single commercially available motor oil that does NOT have any zddp in it.
The problem seems to be that 1200ppm and above is generally considered to be safe, while the latest blends are somewhere around 800ppm. Those are the SN oils. Over in the CD side, they have been reducing the levels as well, so it's not safe to assume that any Diesel oil has enough.
As mentioned above, if your cam is broken in and you are running nearly stock springs you should be fine with whatever.
If you are using big springs and a flat tappet cam you need to be careful.
Another thing to consider is tappet acceleration. Designers have really pushed the envelope closer to the maximum theoretical lifter acceleration rate for the different diameters. Faster acceleration means more force acting on the lifter/lobe interface. Add to this the fact that faster lifter acceleration requires more spring to control the valve and you have a very potent mechanism for cam failure.
One other thing to consider, and that's the consequences of using too much zddp in your engine. It is possible to have too much for a number of reasons.
I find the best information comes from the Joe Gibbs Racing Team. You can say what you want, they have had success and part of that is research. Read here:
http://www.drivenracingoil.com/news/dro/training-center/articles/zinc-in-motor-oil/I don't think there is any better information out there, or a better oil.
R.