I would personally attest to the HU upgrade improving your system's sound.

Until now I'm still running stock speakers on my Jazz. When I replaced the stock Kenwood HU for my present Pioneer unit, the sound of the speakers changed dramatically.

I'm not very picky with sound staging or other SQ terms, so I noticed the sound image is pretty low due to the location of the speakers (at the footwells). But provided I don't crank up the bass and volume so high as to induce rattles, the stock Jazz speakers actually sound fairly decent and clear since the hookup to the Pioneer HU.