Surely it must be either the scoped deer rifle or the AR, as most have stated. I don't know which, though.
At the time, the Kentucky Rifle was the ultimate battle implement due to its accuracy, rate of fire notwithstanding. It could be used from superior ranges with great lethality. It was also a commonly held tool in the hands of the Colonists.
Depending on how you look at that, either weapon could fit the bill - the AR as the modern ultimate battle implement, extremely accurate for a mass-produced rifle with a long accurate and even effective (with the right ammunition, like 77gr OTM etc.) range. Plenty of people own ARs - they are (dare I say) the rifle the Founding Fathers would own today if they were alive.
On the other hand, the scoped bolt gun is probably more lethal at range and VERY common in the US, plus its slow rate of fire would more closely match that of the Kentucky Rifle.
The AR, although used by some for competition & hunting, is more of a one-trick-pony (i.e. fighting rifle), whereas the deer rifle is more of a working gun.
I dunno. This is tough. Can I say both?
If not, I think I'm going to cast my lot with the AR. By the time you get to a battlefield, and a MODERN battlefield, I think it is the one you are going to want to have more. Nobody would have traded a Kentucky Rifle for a musket 230 years ago... but today, I bet more would want to trade a deer rifle for an AR than the other way around once the lead really started flying.
Note: I reject AR10s and M1As not based on their performance but on popularity. It would have to be a VERY popular gun to make the cut, and I think only a scoped deer gun or an AR are THAT popular. FWIW, IMHO, etc. etc. etc.