Engine cleanliness has little if anything to do with the base stock ...
The detergent and dispersent (anti-agglomerate) portions of the additive package are what keep an engine clean. I suppose one could say that a syn has a "better" chance to clean, but that's only because they are designed for longer service intervals, and therefore get more of the additive package so they'll last longer. It's a self-fulfilling prophesey.
However, it's been a while since I've pointed this out, so it bear repeating. Let's think this through, folks.
Presuming we start with a reasonably clean engine, the rate at which the engine gets dirty (soot production, insolubles, etc) is reasonably constant. The engine will not get dirtier, quicker, just because you use a dino versus a syn. So, as long as the oil you've chosen can keep up with the contaminants, either oil should be able to clean decently and keep up with demand, so to speak.
Analogy ... (I'm famous for them) ...
You have a nice clean home. You and your wife are the only ones there. You have a maid come in once a week and clean. She does a good job, and that's all that's needed. Unless your grandkids come over and trash the place, more maids are not needed. Even if you had three maids come once a week (or the same maid three times a week) the contamination production level for you and your wife is fairly constant. Hiring more maids does not clean the house any "better" than what is needed. If the one maid for two people is sufficient, anything more than that is redundant. The extra maids cannot clean up what is not produced past the capacity of the first maid.
Same with oils. A decent engine will not be "cleaner" from using syns under conventional OEM OCIs. Syn's can certainly clean "better" (better being defined as less residual) over longer OCIs because the additive package in a dino is overwhelmed sooner than in a syn. That's simply by design. In short, you cannot clean up what does not yet exist.
Put some ficitious number to it if you want. Suppose an engine creates 35mg/L of contaminants over 5k miles. If the oil has an additive package that is superior to that, then the engine is going to be clean. If a dino can handle 45mg/L and a syn can handle 60mg/L, it's a moot point because both are more than adequate to handle the total contaminant load for the expected OCI. Now, if you were to push the OCI out to 10k miles, then the dino would be overwhelmed where the syn would succeed. But that is not the intent now, is it. The INTENT is to use any lube up to, but not past, it's capabilities. Be it wear, contaminants, TBN, vis, etc. Use a product to it's benefit, but not past. In practical application, the "cleanliness" of an engine is akin to the wear of an engine. As long as you don't use any lube past its capability, then it should perform about as well as any other lube. The thing with syns is that they are made to last "longer", not "better".
I simply do not accept that a syn will "clean" an engine better simply by being present. Once again, it's about analyzing your operations, determining an OCI, and then picking a lube. Just like my signature says.
If you want to artifically handicap the dino by pushing it past its fair limit, the same unreasonable act could be done to a syn. Syns don't last forever, they just last longer. In other words, I could use a syn for too long and make that engine dirty too.
As long as you use a lube within its limits, a syn won't clean any "better", just longer ...