I have both and like them both a lot and consider them equals, although the 338-06 has a slight edge if used at distances longer than say 300 yards, which I do not do, plus it has a better bullet selection.
That said, if you reload get the 338-06 and if not the 35 Whelen will be a better option due to the availability of factory ammo.
Definitely would shoot handloads for either choice. My bolt action rifles see 95% to 99% handloads. Some of them only see factory ammo once in a blue moon to get a chronograph reading with factory loads for reference sake.
With the rise of the “primitive” weapon seasons in some states that allow .35 Whelen from a hammer fired rifle the availability of Whelen ammo is pretty good. Ultimately not really a concern to me, as I have a nice stash of once fired .30-06 brass that would be put to use.
