If the badge got turned into a big item though, I'd stop using it.
The sword or shield are better items when you are low level, but the badge pays off in the long run. A good deal of the time however, I am using all of my inventory slots or need at least one slot empty to rotate things in and out. If the badge is big, it isn't as useful in the short term as another blacksmith prep and isn't as useful in the long term as an extra glyph or shop item.
If you do the math, the 10% damage is better in the vast majority of scenarios and ultimately all of them by end game. However, I have found myself winning more with the +2 sword, because the gains in early game come out to a greater advantage. +10% rarely if ever lets you get an XP catapult and level 1 or 2, but the +2 sword does. Just some thoughts.