Titanium Waraxe

The swinging axe keeps you further back from whatever you are cutting, and it scales better with a harvesting setup. If you have mining speed rolled onto your armor and accessories, this is the faster of the pair. If you are just carrying whatever you happened to craft, the Titanium Chainsaw comes out ahead.

By the time titanium is on the table, trees are not what is slowing your run down. The honest case for building one is that hardmode wood demand climbs steeply once you start large builds and tree farms, and the top ore axes get through a trunk without you thinking about it. The Adamantite version is identical in practice.