What's needed to make this JBL Premium head unit acceptable?

What can I do for my head unit without breaking the bank? If I could get the same sound quality as I had from the JBL in my '11 CM Limited, I'd be happy. I want to keep the head unit because it's needed to control some of the other settings in the truck, but the sound is sheer torture on my ears. It doesn't matter what the audio source is. I've noticed that some songs play at a volume level I can barely hear even when it's turned all the way up. Other times, I can't get the volume level past halfway before the bass gets distorted and my door panels start rattling like a hooptie wagon. I can't tell if it's because I have audio files are mp3, mp4, and AAC format. Has anyone else had this problem?

All I know is I'm listening to the same songs that I used to play in the last truck and the JBL system in that truck had sound quality that was so much better. This music is played from the same iPod and the same Android phone that I've always had.

 

You need something to reshape the signal that your factory/JBL stereo is sending to your speakers. In short, your sound needs to be "cleaned up". Those signals need to be transformed into better shapes. The following article should be useful. You local audio shop should be able to clarify some things and recommend the appropriate signal processor (Audio Control, JL Audio, etc.).Hope this helps!
http://www.crutchfield.com/S-IWT2lEMPVFy/learn/learningcenter/factory/sound_processors.html
for example:
http://www.crutchfield.com/p_161LC2I/AudioControl-LC2i.html