My pet load for my 03A3 sporter .338-06 was a 200 grain Hornady SP, CCI 200, and RL-15 which produced 2900+ fps at the muzzle and was sub MOA in the 03A3 sporter I had. I hunted either with 210 Partitions at 2800 fps same powder and primer or a 225 grain Hornady IB at 2680 fps with CCI 250 primers and W760 powder. I'm within book with the Hornady loads, but over book with the Nosler. The Horandy SP and the Nosler 210 PT are very similar in dimensions with the Hornady measuring 1.212" and the Nosler 1.200" in length, so I tried pushing them a little harder and managed to do so. I wouldn't try it with other 200 gr offerings from Nosler.
My M70 is a little different I haven't loaded for that rifle yet. I bought some Nosler factory ammunition on close out and it shoots well enough I haven't started reloading for it. I tried shooting my pet loads out of my 03A3, but found they were hard to chamber so I decided to start with new brass in my M70. I found the Nosler ammo for $30 and bought 200 rounds, I got 100 rounds ea of 180 and 225 grain Accubond ammunition. This will last me several years as I haven't shot 20 rounds combined through that rifle yet.
Now I don't think by any stretch the .338-06 is superior to the .35 Whelen or vice-versa. Discussing them are like splitting a frogs hair, they are that close. IME the .338-06 handles longer bullets better as every rifle I've owned has/had a 1:10 twist barrel and my Whelens had 1:14 and 1:16 twist barrels. The Whelen let's you have a lot more bullet options when you figure in the variety of cast and pistol bullets you can shoot.
What I've found with both cartridges is they are on the upper end of my recoil threshold as I get older, but they have all weighed in the 7.5-8.5 lbs range. They can get pretty snorty from the bench during load development, more so as I increase bullet weight. So I don't actually enjoy shooting them on a regular basis, and the majority of what I hunt can be handled by much smaller cartridges. The PAST recoil pad definitely helps me more these days than ever before.