No great European experience for myself. But I used a 7x64mm Mauser M03 owned by ErikD for my first Norwegian moose.

I understood from articles in Australia the 7x64 was one of the most popular choices for bolt action rifles at the time. In Germany Per the article. And the 7x65R one of the more popular break open cartridge choices.

Certainly the 7x64 killed the moose easily with good bullet placement.

I have a set of barrels for my Tikka in 12-bore and 7x65R, I have used that set of barrels yet, as the loaded ammo I order, 200 rounds, were supposed to be in stock. They weren't cheap! And then found out it was a three month order. Still waiting 12 months later. Planned to use the ammo, 100 rounds were to be enough anyway, I don't anticipate using it that much. Needed to order 200 rounds to get the order. Then oneday use the brass if when I needed to. I think if it isn't close to arriving, time to cancel the order, source some brass and dies and load my own.

I believe the .30-06 and probably the .308 are popular as well.

I used a .308 Blaser with Sville in Sweden and also his 9.3x74R double. Never even fired them!

I have used a .243 Winchester CZ for Roe deer in Northumberland in the UK. Did not shoot a roebuck. Just three "stalks" over a weekend in a forest.

I think I used a .222, .223 or some 5.6 mm for roe deer in Denmark. Missed a fox. Shot a female roe for meat for the owner.

The 8x57 is said to be one of the most popular choices still in Central Europe. It is the .30-06 of Europe. No doubt some older rifles, but still chambered by smart gunmakers selling in Central Europe.