If cost of shooting is a concern 300's win. I'm from way back when the 06 did okay 300 H&H or 300 W were big dogs and the 300 win mag was okay The ultras came out and I had to have the 30-378 later on The 300 UM is a better choice.
When I was ready for a second rebarreld I considered the 338-378 because I has a couple hundred cases. I decided to sell the W after the second barrel and went with a 338 Lapua.
I do not mind packing big 28 -29 inch guns I never liked the 300 win or the 338 win The case is not big enough to use the slowest powders and big 210,220, 240 in the 30 cal and the 275 or 300 grain in the 338 where they both really shine in the long barrels
Dead is dead, but the 338 lapua is just a fun round