Amp or Speakers?

It could very well be some difference in the "features selected that increase how loud the music is".  Head units, the old one or the new one, have a very limited amount of power to deliver.  The difference you hear is most likely the built-in EQ, the sound expander, the loudness...those features that manipulate the frequency output to make you believe the deck has more power than it does.  Or it could be as little as 1 watt.

On a forum like this, who collectively appreciate the power and great sound of aftermarket amplified car audio, you will find the opinion that you should wise up to the limitations of a factory speakers/any deck combo.  I suggest you look around at the aftermarket systems being used and picture yourself in that category of musical sound enjoyment.  That would include, at a minimum, new front speakers and an amplifier to power them.

...and don't forget the security system!