My first thought here is that Smaug's will is his own and would not be held under Sauron's sway because while Sauron is powerful he is no Morgoth and controlling a dragons is something I don't see possible especially without his ring.
Now as for an Eagle taking on a dragon there is no competition, a dragon is much greater.
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“I wish it need not have happened in my time," said Frodo.
"So do I," said Gandalf, "and so do all who live to see such times. But that is not for them to decide. All we have to decide is what to do with the time that is given us.”
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