Any of the 7mm cartridges would serve you well, and as far as I know, they generally come with a 9.5" twist, so they'll stabilize 175 gr bullets. And even at the modest velocity of 2400-2500 fps you'd get with a 175 gr bullet out of a 7mm-08 or 7x57, lethal range on small-ish animals like what you're talking about is still around 300 meters.
Most rifles chambered in 270 have a 10" twist. If you hand load, you could probably get away with a 160 gr bullet, but mostly you're limited to 150 gr bullets. Not a terrible choice, but it is quite a bit more limiting than any of the 7mm cartridges.
For the purposes of a European hunting in Europe, my vote would be 7x64 or 7x57, but if you're really interested in the 7mm RM vs 270 anything, 7mm RM hands down.
Lots of guys who aren't terribly familiar with ballistics will extoll the virtues of 270 being "flat shooting." While it is a flat-shooting cartridge, most modern bottle neck cartridges are also flat shooting out to around 300 meters, give or take a little. Sighted in for Maximum Point Blank Range, there generally is no more than 5-10 cm elevation difference between any of them at that distance.