I'm constantly going back and forth between these two names. Eleanor is the original form, and the queenly one, as well. However, Elinor is the form that Jane Austen used in "Sense & Sensibility," and I love Jane Austen. :-)
There are also the names Lenora and Lenore, which have both found their way into my Top 10 at different times.
So... which do you prefer?