They both require mezzo-soprano voices with a good belt and an ability to utilize a head voice when needed. You want to choose songs that show off your overall range, and things that are somewhat modern---but not too "pop"--no "Hairspray", no "Little Mermaid". No "Wicked" either--great musical, great songs, but done to death!
Of course some songs I can think of that would be good audition songs for "Aida" would also run the risk of being overdone. The bottom line is to choose a song that really shows both a powerful, beautiful voice AND the ability to express oneself emotionally through the music. You cannot just stand there with a blank look on your face no matter how beautiful you sound--that goes for either ladies' parts.
"Rainbow High" from "Evita"
"Buenos Aires" from "Evita"
Both good for Amneris (but Lloyd Webber is one of those tricky "overdone" composers)
"He Lives in You" from "The Lion King' (music was also written by Elton John--this song was from the Broadway show--not the animated film)--also appears in the show as "They Live in You"
"Shadowland" from "The Lion King" (also not in the movie)
Great for Aida.
Anything else you might already know and can sing that is vaguely similar in style and range of the music in "Aida" should be considered. That way you can just spend the month polishing up the songs to make your performance really spectacular inside of just learning notes and lyrics. Depends on how well you pick up on music.
Also make sure you get any sheet music, backtracks, whatever that you need for the audition. Double check with the direct source for audition information so you know exactly what to prepare for.Will you need to do one song, two contrasting numbers, 16-or 32-measure excerpts?
Then it's all up to the people casting. There is never any guarantee that you will get the role you audition for--if you do, then congratulations. If they pick you for another role, or even a part in the chorus--congratulations. Do the best you can do with whatever they give you. And if you don't get picked at all--well, sometimes that happens. It doesn't necessarily mean you were bad in the audition. A lot of different factors can go into casting that has nothing to do with singing, dancing, or acting ability.