Cobalt Waraxe

This is the tool most worlds reach first after the Wall of Flesh, and the jump from anything pre-Hardmode is large enough to notice on the first tree. Palladium worlds get the identical tool under a different name, so there is nothing to weigh up between them.

Against the chainsaw it comes down to how you hold the button. The saw keeps cutting while you stand still, which suits flattening a whole forest for a tree farm. The axe swings and stops, which suits digging trips where you are also dealing with whatever wanders in.

Do not pay the Goblin Tinkerer to chase a prefix here. Rounding leaves several ordinary speed modifiers tied with the best one, so the first decent roll is the roll you keep.