"Can someone explain the differences in how ZDDP and ZDTP work in a oil formulation, the pros and cons of each if any and if they are compatible together in the same crankcase? Also,what readily available available oil use the ZDTP and possibly why? "
Good question. ZDDP is a zinc, sulfur, and phosphor compound, an organometallic salt, dissolved in the oil, usually as an ester. It's real name is "zinc diaryldithiophosphate." It has been used since the early fifties as an AW/FM additive, an anti-oxidant, and anti-corrosion additive; a "multifunctional" additive. It is mostly used in dino oils but in some synthetics as well; synthetics that use low ester percentages.
ZDTP is a "phosphonate" (instead of a "phosphate") and is similar to the above ZDDP. It's primary use is in high ester full synth formulations because that form of zinc seems to work best in reducing friction and wear in high-percentage ester/PAO formulations.
Both of the above form a layer of ferrous sulphate or phosphate just above the base layer of steel or iron. The sulphur ions in the "thio" portion then attract the zinc molecules of the metal to bind them. So what you have is a three-layer system with the top layer as the softer metal zinc providing a low friction surface to prevent steel-to-steel contact.
BTW, the whole "phosphonates" series have been shown to be better in reducing friction for high ester oils.
Now Moly and Antimony work the same way, but generally at higher temps and at higher loads.