subdivided into 3, but you wouldn't be counting each of those subdivided beats as 1, 2, 3, 1, 2, 3, 1, 2, 3...unless you are a psychopath. The "feel" of the song is in 2 or 4 groups of 3. Putting it in 3/4 kills the musicality of the song.

Ask your mom which time signature best communicates the feel of the song. If she handed sheet music to a student to sight read (assuming the student had never heard the recording), which time signature has the best chance of resulting in that student playing the song as the Billy Joel intended?

I think 3/4 will sound more robotic. See what she says.