Which 338? I assume you mean 338 WM.
I've owned both 338-06 and 35 Whelen in the past. Still have the 338-06. Lots of guys buy them because they think they will get get improved perormance over a 30-06, with less recoil than magnum rounds. You don't. With modern 200 gr bullets loaded in a 30-06 it will outperform either. At ranges up to 100-150 yards the 35 whelen and 338-06 have slightly more energy if loaded with 225-275 gr bullets, but all 3 have more than enough to get the job done up close. The more aerodynamic 30-06 will pass both of them in trajectory and energy before the bullets get 200 yards from the muzzle.
Recoil, there is no free lunch. When firing 200gr+ bullets both the 35 Whelen and 338-06 generate far more recoil than a 30-06 firing a better performing 200 gr bullet. In fact they generate slightly more recoil than a typical 300 mag firing a 200 gr bullet.
There is a reason they never caught on. Both 338-06 and 35 Whelen have had short runs of factory rifles and ammo from time to time. Ruger and Remington have made 35 Whelen rifles in the past, but neither are currently. Weatherby made a short run of 338-06 rifles a few years ago, but both should be considered handloaders rounds.
That is not to say a 35 Whelen is a bad choice. For someone just wanting something different it is a good round. It will certainly take any animal in North America, trajectory is a minor handicap, but good enough for most shooters. I bought my 338-06 simply because I liked the rifle and the round. I like being able to hunt with something just a bit differernt than 99.9% of the other hunters are carrying. I bought the 35 Whelen for the same reason. Sold the 35 Whelen only because I liked the other rifle just a little better and could not justify keeping 2 odd ball chamberings.
Just about any round from 308 up to 338 WM has more than enough power to get the job done on all North American game. I believe in choosing chamberings because you like them. If you like the 35 Whelen, buy it. Just make sure you buy it for the right reasons.