I shoot 7X65R, 8X57JRS, and a lot of 30-06. There is not much difference in them with factory loads, although the rimmed 7X64 and rimmed 8X57S versions as above are loaded about 10% milder than the rimless versions you'll be shooting.
In reality I'd feel more comfortable with a 30-06 with a healthy 200gr Partition.
I'd worry a whole lot more about claws and teeth and less about recoil. A 180 Partition is a good compromise, IMO.
...just an opinion for what it's worth.
