My father felt similar about his 7mm-08 Axis until he put a better scope on it and it's now a keeper. Speaking of an improved Savage, I have the Weather Warrior in the same caliber. It is stainless and has the accustock and accutrigger. It does shoot better thanks to a lighter trigger and a good scope but is noticeably heavier. The weight doesn't matter to me but can to an older man.
If your wanting to get a .300 win mag keep the Axis and you have a lightweight backup rifle with hardly any recoil and plenty of power. Option two is buying an improved 7mm-08 rifle.