I've upgraded my first upgradable sword some, and I can't notice much difference. The pixelated one that you have when you're hurt looks very upgradable, but the giant one seems to look the same, even if I have a wood sword.
Does upgrading improve both, or is the giant one just the best that it can be? What if I change weapons and buy the Claymore from that guy in the middle of nowhere, would the fully-healed version be better then?