Can only go on what I've heard, read, and what I've seen from a similar cartridge, the .358 Win, in the hands of a good hunting buddy.
My buddy nailed well over a dozen elk, as well as black bear and deer with his .358 Win, a Browning BLR. Took them cleanly from hide-scorching range to a bit over 200 yards over the years, rarely with a second shot. Believe he used the Speer 250 grainer for a while, then switched to a 225 grainer - sorry I don't know the make of that one. Either way, he made a lot of great one-shot kills on a variety of big game at realistic distances.
The .35 Whelen churns up a bit more velocity than the compact .358 Winchester, so I'd expect it to have a solid 250 yard effective range, or perhaps 300 yards from a good rifle, with a good shooter. As far as game, I'd carry it for anything in North America, loaded with premium bullets.
My old '06 is about due for a new barrel, and it's a tossup between the .35 Whelen and the .338-06... Whelen has the advantage of factory ammo being relatively easy to obtain. The .338-06 has the advantage of a higher sectional density for the same bullet weights.
Sorry, no direct experience, but I sure have looked at this cartridge as a suitable candidate for a general purpose elk, bear and deer rifle.
Regards, Guy