Well, as I stated, almost everything is a trade off, but the short answer is "yes".
I guess we'll have to get into the basics of oil constuction. And rest assured, there are others here to know better than I.
All lubricants are manipulated before going to market. We don't use anything as mass-market consumers that isn't modified in some way. The reason I point this is two-fold. One - to state the obvious so that they who would nit-pick are going to have to accept I don't have enough time/space to cover everything. Two - so that you understand each product is made to a specific target market, typically based upon price point.
OK - that out of the way, let's consider:
Things oil does by innate characteristics: Oil lubricates. Oil cools. Just by being present, it does those things. Even with no additives, it will do these things. It can do them BETTER with some additives.
Things oil does only with the assistance of additives: Oil can clean. Oil can disperse and control.
Things some oils do well, and others need help with: Oil reacts differently to temperature depending upon base stock. Ah, yes, the ever present topic of synthetics.
Group III - highly refined base stocks (severly hydrocracked). Group IV - PAOs
Group V - Esters, etc and GTL, etc
Many of the additives have multi-duty functions. Many can not only fight corrosion (base chem's) but also help with lubricity. Others can help with cleaning. The list goes on and on.
To answer your direct question: "In this comparison, would a HDEO be trading higher zinc for a lower concentration of another additive and vice-versa for synthetics?" all things have to be considered as a whole, and not individually. Zn is only one example of the individual disparity of additives, even though the whole package performs well. But my answer is "yes" because all things are a balance between targeted performance, and cost.
Dino HDEOs have more VIIs because they need them, where PAOs don't need near as much. But, PAOs cannot hold detergents and dispersents in suspension very well, so you'll always have some amount of group II, II+ or III mixed in with a IV.
To be honest, as I said, I'm not a tribologist, but I am smart enough to know what I don't know. I accpet that the true chemisty escapes me at times, but the concept does not get lost on me.
Will there be more of one product in a dino HDEO and less in a syn? Certainly. But again, it all goes back to the target market. And all they need do to make up for some (perceived) lack of characteristic "F" via a lower content of item "A", is to bolster item "Q" which nets a similar or same result. (FAQ - get it?
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I guess what I'm trying to get you to understand is that I doubt you'll ever see much difference in a dino HDEO versus a syn as far as cleaning goes. They both will perform very well. If those are not enough for you, then you might consider a product such as ARX, which I have had great personal experience with. It is an extrodinary, soft-touch approach, cleaner.