I have hunted with both. I used to hunt with an older steel receiver BLR in 358 Win. Now, I use a Ruger 77 in 350 Rem Mag. This may sound strange (given what I had and what I now use) but given the parameters that you've stated, I think a 358 Win. would be ideal. It accomplishes virtually the same thing as the 350 Mag but with less powder and muzzle blast within the short to medium range category. I also found the Winchester 200 gr Silvertip load for the 358 Win. to be much more accurate in the BLR than the Remington 350 Mag 200 gr load in my Ruger. Of course, if you don't reload you'll never realize the best that either cartridge offers, not to mention that either one in factory ammo is relatively hard to find and costly.
I sold my BLR because someone offered me considerably more $ than it cost me. So, when the 35 caliber bug bit me again years later, I opted for the Ruger 350 Mag, since it was easy for me to obtain at Wally World of all places. Though I really like my 350 Mag, I have to admit that everything I've taken with the 350, I could have just as easily gotten with the 358 Win. I must also state that I hunt only deer and hogs.
Not to confuse things but the bottom line is what some of the others have stated about either caliber being ok for what you want. So, it's nice to know that you cannot make a bad decision. Good luck.
