You can get by with converting from aac to mp3 and maybe not hear any significant loss in quality depending on the song, but this is a bad idea. Both are lossy formats which mean they have taken a huge song file and run it through a complex process to strip out much of the data stored in the music and keep the parts necessary to make it sound good enough for your ears. Now what you are trying to do is take one highly compressed file and move it to another compressed format. Ideally you would convert to either mp3 or aac from a lossless file format (FLAC, Apple Lossless, etc.) or the original cd - but not convert between them.
Here is a good article on file formats: http://www.stereophile.com/features/308mp3cd
The article has some in depth acoustics data, but you can read it for the main gist. The aac (mp4) file format generally gives a better sound with a slightly smaller file. So unless you have a device that is not compatible with aac, there is no reason to be converting to mp3.