Technically, AAC and Apple Lossless (ALAC) are separate codecs.
AAC is a newly developed codec by a conglomeration of several companies and is used with the MPEG4 ISO standards. It is not proprietary to Apple. See:
http://www.apple.com/quicktime/technologies/aac/
http://www.vialicensing.com/products/mpeg4aac/standard.html
ALAC is an Apple proprietary codec. See:
http://craz.net/programs/itunes/alac.html
Song file size is a factor of bit rate and song length. Audio quality is a factor of bit rate and encoding format. AAC and MP3 formats are considered Lossy, as they sample the target music file and reduce the total size with some reduction of audio quality. Lossless files are considered CD replicants as they contain all the digital data on the original audio CD. They can be fairly large in comparison to the traditional Lossy file.
Encoding a music file into a Lossy compression format will strip details from the file.
Transcoding from one Lossy compression format to another Lossy format will compound the loss of details from the file. (eg: transcoding a sound file from: AAC to MP3; or MP3 to AAC). The audio degradation becomes more apparent when transcoding files ripped at lower bit rates (less than 192kbps).
When you burn an AAC file to CD and then re-rip the CD as AAC or MP3, the sound you end up listening to will have gone through a lossy compression process twice. Those losses can add up, taking what were only mild or even unnoticeable deviations from the original sound after the first phase of compression and making those deviations much more noticeable and objectionable. This is especially true if you try to take music at a low bit rate like 128 kbps (what Apple uses for iTMS) and try to compress back down to the same low bit rate.
The preferred method is to save all audio "masters" in a Lossless audio format such as Apple Lossless, WAV, AIFF or FLAC (or the original CD), and then transcode directly from the Lossless source file to your preferred Lossy format such as MP3 or AAC. This procedure preserves as much of the original audio signal as possible and prevents the
compound loss of audio details from the file.
The generally accepted theory is that AAC/128 sounds as good as, or better than MP3/160 (and possibly even MP3/192). Transcoding your AACs/MP3s will most likely result in noticeable audio quality degradation. But -- test it out for yourself. If you cannot hear the difference, then it may be acceptable. Bear in mind that any improvements &/or upgrades in equipment (iPods, headphones, your ears, etc.) may uncover the
additional audio limitations you created
at a later date.
Lastly, see:
Choosing an Audio Format
I import all CDs into Apple Lossless for archiving and converting to various Lossy formats as needed. All my iPod music is in AAC/256/VBR. I can hear the difference. Others cannot.