No experience with the single shots, but I used to own a 35 Whelen and have had 338/06 as well. They are both fun, interesting rounds that will work. With the right loads they are not too big for whitetail and both shoot a lot flatter at longer ranges than most folks realize. Perfectly adequate for distances most of us shoot, and suitable for any North American game.
On the other hand neither offer any real advantage over a 30-06 when loaded properly. The older 06 will shoot flatter with lighter bullets, has much less recoil, and is every bit as effective on larger game when loaded with heavier 200+ gr bullets.
The 35 Whelen recoils at 300 magnum levels, (probably much worse in a lightweight single shot) ammo is harder to find, selections are few, and much more expensive. While factory ammo is available, it should really be considered a handloaders round.
In short, it is a good round that will get the job done. If you want one then go for it. Just keep in mind a 30-06 does the same job with a lot less drama and expense. Depends on why you want the round.
