Actually, if an ants armour was as thick as a Tank, it could withstand roughly the same level of punishment, the difference is that an Ant is sentient, and would therefore rather preserve its own life.
Someone already mentioned Spider Silk, which is stronger than any metal-based fibre known to man, though, I think, some organic compounds can take more punishment. Certainly, if you think about things on a cellular level, biological tech has disadvantages, but remember that a cell is a collection of organic compounds, not a compound in and of itself, if something were engineered to grow chitinous plating that was 4" thick on its carapace, I think you'd be surprised as just how tough it was, especially with a softer, absorbent later underneath to soak up impacts.
Look at it this way, 200 years ago, metal would never float, so we built all our ships out of trees.