Of course.
There is also a VAST difference in soil quality between the river bottoms of Western KY and mountain hardwoods of East KY.
But I don't believe there's so much difference between the soils on those far West TN counties bordering the Mississippi River vs. West KY river bordering counties.
The bigger difference than soils (between those TN counties vs KY counties bordering the same River) is antler high grading by TN hunters. This is mainly resulting from the differences in deer hunting regulations, and am not saying TN is wrong nor KY correct, just pointing out that hunting regulations do make differences, often trumping the differences in soils.
There is also a difference in hunter "mindset" when comparing hunting in TN vs. KY. The same TN hunter tends to raise his shooter buck standards when he hunts KY. But again, this is in part due to differences in the hunting regs. Those who live & hunt anywhere along the TN-KY state line see this, even in Middle & East TN, not just far West TN.
I agree 100% that the soil composition on one side of the river is no different than the other side. That river has flooded so many times throughout history that the entire river valley has the same sediment. The people who inhabit it are the same, too, regardless of which side they reside. The river doesn't segregate families and friends to create a border between cultures or beliefs, so I find it hard to believe hunters are that much different in mindset. That leaves only one difference that could reasonably result in bigger deer in KY than in TN, and that is regulations.
Unless something changes with regs we'll never know. Imo, the worst thing a state can do is allow long fun seasons that overlap the rut. I whole heartedly believe anywhere from PA to IA dow to LA, within proximity of the major river sediment bottoms, could produce world record class deer if the herd and seasons were managed to allow deer to reach maturity. Imagine what bucks would suddenly exist in west TN if only does were hunted for 3yrs., no bucks. I don't think it's a stretch to think a new world record typical could be killed that fourth year.
That all said, all of TN does not have that same potential. Most of it does not. But that's the same for every state. All of the big buck states have one thing in common. Their "trophy" zones are the part of the state that is bordered by a major river. The ones that produce the most big bucks are the ones with shorter gun seasons that occur after the rut.