Are some of these more inherently accurate than others?
- no, not until you get into $3000 benchrest rifles
Do some lose fragmentation around certain distances?
- depends entirely on bullet weight and design for each chambering. Not an issue either way.
In other words, which one is the most likely to cleanly take a deer at the furthest distance? Which one is least likely to do it?
All things being the same...premium bullet, shot in exactly the same place, etc etc, then more energy = more potential to do deer dropping damage. When energy levels are nearly identical, wider bullet tends to do better. Exactly how much width equals how much energy is undetermined.
So this means a 416 Rigby gives a minuscule edge on dropping a deer cleanly as compared to a 30-06 or 243 or whatever, right?
NO. Shooter is a human right? Humans are impacted by recoil. Heavier recoiling rifle makes it more likely to develop flinch.
Heavier recoil means a slower follow-up shot if one is needed. If the user is already winded from say hiking up a hill to get the shot, this is greatly increased.
Even if there is no flinch, heavier recoil fatigues the shooter more than lighter recoil. This affects how well a shooter can practice and how long a shooter can practice. Regular practice is probably 100 times more relevant to which is going to give you the best results vs which cartridge is best for dropping deer.
This all favors a lower recoiling gun, which equates to a lower powered cartridge.
Added onto this, what is the cost of loaded ammo, what is the cost of components for handloading?
In general, this also equates to a lower powered cartridge.
Honestly, in the hands of a very skilled shooter who shoots regularly has no flinch and cost to practice is irrelevant, the 30-06 is probably on top.
But here's the other thing. The difference between best and worst among that list is astronomically small. (Assuming equal quality load, bullet, etc)
I'd rate the best at 99.9999999999
I'd rate the loser at 99.9999999998
Once you have 'enough' power, while extra power is in theory good, the change is so small as to be irrelevant.
So once you go back in and factor in the human susceptibility to recoil, economic factors, and the like, the lowest recoiling round that cleanly gets the job done actually wins out. That's why I'd add something like the 257 Roberts, 25-06, or 250 Savage to your list and crown it king. Because a guy with the quarter bore has more than enough power (those round can all take elk) and the recoil is low enough which means you gain more on your trips to the range, and hopefully you make more trips.