I don't use a .35Rem, but I do use a .356Win. Different but the same. Little faster, not much, but the same bullets.
The .356Win has been my primary for the last 20 years, but for the last 2 or 3 years I've been using a .30-30 pretty frequently. I switch between 200gr JSP and 250gr JSP for the .356, but I only use 170gr PP for the .30-30, and that's just because there's not been a heavier factory round.
Most of my hunting for the last few years has been hogs because I've got a friend whose farm I help to keep cleared. I've shot many deer, but no bear with either of these guns.
I've not lost an animal that's been shot with the .356, and the great majority of them have been DRT. I've lost one or two hogs using the .30-30, but I am convinced that was due to poorly placed shots more than any other consideration. Poorly aimed and rushed shots in low light. I've had at least one such shot that I can clearly recall with the .356; he was running and I was in a tree-stand with about 13-inches of lateral "swing" but the brute didn't take another step after a 200gr bullet passed through his neck behind the skull without breaking the neck. I don't know why he died, but he did. Concussion maybe.
I don't evaluate bullets and shots on game with the same educated scrutiny that Joe does. I only use: Did the bullet go where I aimed it; Did it go in deep enough; Did I kill the beast; and did I have to chase it. Beyond that, I know nothing.
I do know that bigger holes bleed more and that shot placement is everything. My .356 has never failed me, and my .30-30 has never failed me when I did my part.
Down to brass tacks... I'd pick the .356 every time if I had any doubt about which one would absolutely positively do the job.
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