That's something that should be studied. How much does bullet diameter make up for placement errors? How much does velocity, energy?
My guess on the width part is it'll make up for the error roughly as much as the larger diameter projectile creates a larger permanent wound cavity, which is to say for the most part 1.5-3x bullet diameter, so.. an inch at most.
To elaborate a bit more, where caliber size can help- with bullet construction type equal- is having more energy to transfer to the CNS and more material to reach out a bit wider and deeper.
A 195gr TMK from a 308 at 2600fps MV compared to a 77gr TMK from a 223 at 2600fps MV is a good example. Both bullets are constructed the same, for all intents and purposes. They'll both behave very similarly in regards to how they start expanding and shedding weight and transferring energy via hydraulic force and loss of forward momentum.
So let's compare the ballistics of the two at 250 yards. The 195gr TMK, having more mass and a higher BC, will be at 2247fps and have 2186ft-lbs of energy to work with (doesn't mean all that transfers to the animal). The 77gr TMK will be at 2097fps with 752ft-lbs of energy to work with. Even at more equal impact velocities (2240fps), the 77gr TMK still only has around 860ft-lbs to work with.
The TMK is very efficient at transferring the energy it has into the animal, and with far less mass, the 77gr would be more likely to not exit and transfer all 752 or 860 foot pounds compared to the 195gr which is more likely to exit from a whitetail and take some of that energy with it. It's still going to transfer more than the 77gr though in most scenarios. It also has more material and will be ultimately more forgiving to shot placement errors and produce wider wounding most times.
You'll also have more range ability from that 195gr TMK load as well due to the higher BC and more retained velocity and energy as a result. The overall result of either at like 100 yards or so would be hard to discern between. As you stretch out the distance with the 77gr TMK load, you'll see less and less reliability and consistency to the animal dropping or dropping quickly. With less energy being dumped at once, you're relying more on rapid blood loss vs shutting down the CNS while it bleeds out. It'll also be less forgiving to shot placement errors and the little bullet can end up more off your mark at further distances compared to the higher BC 195gr TMK.
Hopefully I'm making sense and you're getting the point here lol. Keep in mind too this is comparing like bullets. If you compare the 77gr bullet to a bonded or copper bullet even, or especially, of a larger caliber, things change a lot in how the compare and contrast.