At least, this is what Douglas Anderson has to say on the subject:
Some Tolkien commentators, including Robert Foster, in his "COmplete Guide to
Middle-Earth," have been tempted to equate the Lord of the Eagles in "The
Hobbit" with Gwaihir the Windlord, the eagle who rescues Gandalf in "The Lord
of the Rings." However, this cannot be the case, for in Chapter 4 of Book V in
"Return of the King," "The Field of Cormallen," Gandalf says to Gwaihir, "Twice
you have borne me, Gwaihir my friend." The two pervious times were demonstrably
Gandalf's escape from Orthanc and when Gwaihir bore Gandalf to Lorien after
finding him on the peak of Zirak-zigil subsequent to his fight with the Balrog.
These two instances exclude the possibility of Gwaihir being the eagle who
rescued Gandalf in "The Hobbit.
I'm new to this board and don't feel qualified to venture an opinion of my own,
but I thought I would throw out that little
tidbit.
