At the end of the day, it's not your equipment that matters. It's how you use it.

There are plenty of things that go into how materials interact with one another. A powerful sword, if it scores a direct hit against a shield, might break it apart. But it could also hit the shield on the side or slip harmlessly off the wood. The strength of its wielder also matters; no sword, no matter how strong on paper, can hurt an opponent if it's wielded by someone who lacks the strength for it.

And there even comes a time when different strengths stop mattering. Against simple cloth, for instance, a sharp iron knife probably cuts just as well as a sharp mythril one. And a bronze sword could probably withstand roughly the same number of hits from an iron sword as it could from a titanium one; the difference in this case would be the amount of damaged suffered by the iron sword in comparison to the titanium one. They would both deal similar damage to the bronze (alright, maybe the titanium will do a little bit more), but the difference lies in how much damage each takes in return.

So the advice is this: don't worry too much about the way materials interact. If you're a swordsman who wants the most powerful sword out there, you're going to want adamantine sooner or later, we're all sure of that. But don't expect your super-powerful sword to mow through your opponents without requiring a little bit of work. At the end of the day, your scores will be what matters.

As for the battle you're in now: judges know to take equipment into account when considering whether characters were acting realistically. If your opponent is letting her inferior equipment take tremendous amounts of damage without breaking, then a good judge will penalize her score. Chances are you'll win in the end!