First off, leaving out the car setup, COG, etc. it is only the compound that matters. Coefficient of friction and the material shear strength are really what matters. The problem with this is that the highest friction materials with adequate shear strength will not provide much of a tire life. Once you factor in a material that has adequate tread life (say 30 to 40k miles) that has all of these above properties you can compare them.
For standard road driving, you will have to deal with imperfections in the surface, like potholes, bumps, chatter, etc that we all find when driving. The tire and compound and aspect ratios we have picked all can handle the lateral force that we will put on it up to the point where it exceeds the COF. This means they all will corner right up to the same cornering g-force before you skid off the road. The aspect ratio in this range is about 15-70 or so due to mechanics, but that is another story. This range of aspect will all have the same tire height for our comparison, so just say they are all 30" tall, so the COG never changes.
This means on a perfect road they will all corner exactly the same. The lower profile will feel more snappy and responsive, due to the least amount of movement required to load the sidewall into the turn, but does not effect the cornering ability. This also feels more responsive for going through a s-curve when transferring weight directly from one corner into an opposite corner. Again, the cornering ability is not affected though.
Once you put this on a regular road with imperfections, it simply becomes a matter of which tire stays in contact with the road, since the cornering is equal in all of them, for a tire in the air handles ZERO lateral force. Super low profile tires have virtually zero ability to respond to bumps pneumatically, instead depending on the suspension alone (remember that this car always has the exact same suspension system). Pneumatic response in a tire is always faster than suspension response due to the suspension have to transfer weight. High profile tires can absorb more irregularity and stay in contact with the road better, but they run into the practical problem (not theory) of tread rolling to lose contact. This really starts happening at about 75 profile with modern manufacturing techniques.
So, the question is, out of the tires that all give us the same ultimate cornering that we want, which will stay in contact best with the road surface as it changes? Factoring in the two limits from above, this is generally in the 50 to 60 aspect with current manufacturing.
F1 and Indy use 50, NASCAR use 54.
I wrote a bunch more, and I got logged out so I am just putting in what I had in my clipboard :-(
After several paragraphs, here is the bottom line. Properly inflated tires on a standard car: 50-55 on the front and 55-60 on the back will give you the best cornering on regular streets.
Please comment if you like.