AAV Vs MPEG

Various factors.

If you created one file from the other format, the original file will be of better quality. If you created both from the same original full-quality source such as a CD and both have the same bitrate (you can check in iTunes), the AAC will be of better quality. If they came from the same source (e.g., CD) and they are of greatly different bitrates, the higher bitrate one.

If I convert a file to a different format (e.g., because my mp3 player does not support AAC) I always make a note in the comments about the source so I know which is the better quality. Converting a 128k bitrate AAC to a 256k MP3 does not improve the quality.

It sounds to me like you need to hone your general Mac administrator skills and set up a guest account for your grandkids. They didn't harm much this time but you wouldn't want them locking everybody out of their accounts. Make sure you are admin, then give restricted use accounts to others. You can share iTunes media between accounts but you don't want them deleting your music -- and bookkeeping files!