I know the topic is specifically about who was greater, but its still interesting to talk about who was more evil.
The point that Sauron was not able to completely control the Dragons suggests that they were more independent than the Balrogs with regards to their choices. Now, if the Balrog is completely under the sway of Morgoth or Sauron, can it be considered liable for its actions? I would say no, the Balrog has no choice but to act according to Morgoth/Sauron's will.
Dragons though, being more independent, seem to have greater responsibility. They seem to choose to be evil in a far more obvious way than Balrogs do.
Now, this can be concluded in two contrary ways, depending on your definition of evil. Balrogs can be considered slaves to evil, and thus less evil than the Dragons who choose evil. But conversely, Dragons can be considered flawed (extremely flawed!) beings who retain the chance of doing good. Balrogs can never do this and thus are more evil.
Which one?
