I thought it was strange that off all the places in Spira to hold a concert where many people will attend, they decide that the Thunder Plains was the best choice.

WTF made them think that was the best place? I thought the Luca Stadium would have sufficed, but no. Let's have all the concert goers stand out in the rain while Yuna sings her pretty little song, and lighting crashes all around the plains.
I was wondering the same thing for quite some time, but if you remember at the end of the song the thunderstorm stops and the sky clears up. So I'm guessing that they wanted to have it their so they could add that last scene, and make it feel that much more epic with her stopping a storm that has never stopped before with just a song.

To the thread topic:

Yes I thought they could both sing very well, and I think the scene was added to give a background story on what happened to Lenne and how her & Yuna are similar. (I could be wrong though because I didn't finish this game)