I have shot both the 358 and the 35 Whelen.
The shorter cartridge will work well on animals up to the size of moose within 175 - 200 yards. The charm of this round is that it can be chambered in light lever actions like your '99 or a Browning BLR. I personally think it never got really popular as the recoil can be stiff, especially in a light rifle like the BLR.
The .35 Whelen is one of the most underrated cartridges ever developed. It is not overly fast or particularly sexy and doesn't have the magic "magnum" word in it's name. It has an honest 300 yard reach on moose-sized animals which BTW is 150 yards further than the typical hunter's ability.
Big heavy bullets at moderate velocity penetrate better than faster, lighter projectiles contrary to what the fans of Roy Weatherby claim.
The 358 Norma runs about 150 - 175 fps faster then the .35 Whelen. This is a fairly significant step up in both performance and recoil. Good quality bullets are a must especially if there is a chance to encounter a heavy animal at very short ranges.