Originally Posted by saratoga
Honestly, I kind of want to see what you think a digital to analog converting cable looks like.
The cassette adapter is louder because the preamp that the cassette head outputs to is very sensitive. Also, since the interfacing isn't done directly, some intermodulation distortion appears which makes sound brighter, so it seems louder.
The AUX jack is the "cleaner" solution, but if your MP3 player can't output a high enough signal for it, try using a headphone amp with it. Fiio amps are good and very very cheap.