For me, European.
I prefer European traditional hunting cartridges, more then military cartridges used for hunting, and more then european military cartridges used for hunting.
That is in theory and preference, only.
But, first priority is availability of cartridge in local shops. And when it gets to final choice of caliber, I will opt for vannila caliber, available locally, sufficient muzzle energy for specific hunt, regardles of its history and origin.
An example, I was dead on, focused, to get myself allround boltaction, in 7x64, true European hunting caliber.
But, when I was not able to find it, I took the same in 30-06. Due to market supply. No regrets
Lets see some popularity, of some cartridges from my perspective.
Rimfires:
22lr (american) - no competition in European caliber
22 wmr - ditto
Pistol and revolver cartridges:
9x19 (European) - no competiton in American caliber
45 acp - (american) - no competition in European caliber
44sw - (american) - no competition in European caliber
38 sp, 357 mag, 44 mag - (american) - no competition in European caliber
Pistol and revolver world is ruled by american calibers.
But none of them approaches popularity (and cost) of 9x19
Rifle:
6.5 class
6.5x55, 6.5x57 vs 6.5 creedmoor. Nordic countries 6.5x55 wins popuarity, but for the rest... I would say 6.5 CM is winning present lap of poplarity race. Use of 6.5 is limited, and with energey on lower end for all round rifle. In many cases it will be for roe deer, a second rifle, and big brother in Europe will alwasy be something from 7mm up. In a small 6.5mm hunting world, 6.5 CM is gaining fast. Today 6.5 cm is fashion, we are yet to see if ti will become classic.
7 mm class:
270 win (american), in competion with 7x64 (european) - 270 more popular in US, 7mm x64 more popular in Europe, but I am under impression, 270 is gaining in popularity on expense of 7mm x 64. To add 7x57, is incoparable, this caliber is loosing popularity all over, many factories do not produce any more rifles in 7x57.
7-8 mm class:
30-06 (american) vs 8x57 (european), 30-06 I would say, 50-50% in popularity on traditional EU continent, but 30-06 is gaining popularity slowly and steadily. For America it is absolute, ultimate caliber - 30-06.
8x57 not popular in US, helped by fact that some american factories offer ammo with inferior powder load, reducing performence down from true pottential.
Then we have class of 9.3, a european turf.
From American calibers, hard to find similar, maybe 35 Whelen. It is my impression that 9.3 class are definitely on European side of popularity, on both continents. 9.3x62, mostly. There is also 9.3x64, ballistic equivalent of 375 HH, but in popularity is very shy. Few facories make ammo for 9.3x64. (for euroepean hunting, is a bit too strong, for Africa, is not everywhere legal for DG.)
Break actions
Then the rimmed. flanged cartitrdges - for break actions.
Definitely, popularity is on european side. Most of break actions, still popular, traditionally come from europe and UK. SO, european flanged calibers win popularity contest here.
Magnums.
Hmmm.
300 win vs 8x68.
300 win mag, wns popularity contest.
8x68, is still there, but becoming scarse. Only few factories make ammo for 8x68
So this is from my perspective, estimate. Could be wrong. There are hundreds of cartridges world wide, went quickly trough most popular ones that came to mind.