Keep in mind, the 8mm-06 has a better sectional density than the .338-06 in same-weight bullets, and the 30-06 has even better!
You can generally drive a certain weight of bullet faster in the larger caliber, so that somewhat mitigates the "benefit."
A 225 gr .338 bullet has a SD of .28135, and the .358 is .25059.
But the 250 gr .358 is .31261.
You said 35 Whelen Imp, which to me says 250gr @2650 fps.
Compare that to the .338-06 225gr @ maybe 2650-2700 fps, right?
I think I'd go with the Whelen, since they'd both work great, and you have an eye on close shots with bears.
As for recoil, similar powder weights and bullet weights should give similar recoil in the same stock design; the main difference here would be if you go with a heavier .358 bullet, which may give you a little more push, but both of these guys are right there with the '06, so don't worry much about that. There might be a 5% increase going from 225 to 250 grain.
As for trajectoies, if you don't have a ballistics program, give me the BC's of the bullets you plan on using and I can figure it for you.
If you're thinking of building a .338-06, you have to ask yourself how close is this Whelen to what you had in mind - chambering aside.
Because even if it was in .338=06, but the wrong action, bbl length, etc., you won't be happy.
Cheers!