24 bit sounds the same as 16

First the old files were 16 bit changing them to 24 bit does nothing but make them bigger you can't improve sound quality by making them bigger. "if you pour one gallon of water in a two gallon container you still have one gallon".

Now your not going to notice that big of a difference using 24 bit in a home studio ( just my opinion) but if you got the space it's certainly won't hurt. Seeing you final product is mp3 your problem most likely is happening between the mastering and final mp3 encoding. Before we go further how does the song sound in itunes as Aiff next how does it sound in itunes as mp3?

One of the things itunes can do is add EQ to a song when listening. Could be the aiff is set different from the mp3. Another thing is check the garageband > preferences > Advance and check the Export Project At full Loudness.

You may also want to try a different audio editor to do mastering of the .aiff.

one obvious question is; how much are you compressing the file? what are the mp3 settings?

Part of the problem, as I have come to know it, is the way in which it is compressed and use of something called "dithering". There are several algorithms used for dithering a file down to the MP3 compressed file and the most well know is "pow-r dither" . It will reduce the file size without destroying the audio. To use this properly, you need a good stereo file editor. I use Peak Pro (5.2) and it does a great job of mastering my files for distribution. It comes at a steep price however ($400-600 depending on your student status). There are free editors available such as Audacity and I would strongly recommend using them for your final mastering step and conversion to MP3 and not rely on Itunes or Garageband to do that for you. This should allow you to get significantly better quality.
The loudness problem you speak of is a result of the volume wars which have forced more and more bands to compress the heck out of their sound. This is the type of compression that makes your track louder it is not the same and the compression that is used to make your files smaller(as in MP3). It can all be very daunting and the learning curve is steep. I have been working with compression for years and I still feel like I only get it right 75% of the time.
So, get a good stereo file editor for you MP3 compression and look into audio compression to increase your loudness.
You could just not participate in the war as a conscientious objector as well.