Balrogs, being
Maiar are extremely powerful and have great power that they draw from
Melkor, their
Vala. That is why I think that Balrogs have more power than
Dragons. Dragons are created with power, and they have power, yes, but not as great as that of who created them.
Since Balrogs are Maiar, I assume, like every other
Maia, they draw power from their Valie or Vala, and because of that, they are able to have strength as though they are one of the
Valar, and knowledge, and wisdom, and guidance. Dragons live and fight off of their own energy and power, while Balrogs draw from the much bigger force of their leader; Melkor, I believe.
The size does not matter, the power does. If a
Balrog is able to harness and draw from Melkor more power than a
Dragon, then that Balrog is more powerful, regardless of it's stature or size.
Again-- this is mostly speculation from me, but I am quite sure this is how Maiar work.