i thought about the 338-06 too but it seemed like the 338 fed would be more efficient in a short, say 18" barrel. I love short, handy handis!
Either the 338 Federal or 338-06 would be an excellent choice.
If you hand load then ammo isn’t a problem in the least bit, but if not then the 338 Federal ammo is cheaper.
I hand load my 338-06 A-Square using once fired 30-06 Springfield brass with excellent results, but that’s in a Weatherby Mark V Ultra Lightweight, not a Handi.
yooper77