I just hear a different arrangement and mix. There are spots in the 'clean' one with complete silence. I also hear how everything lines up on beat and crisply decays on beat too.
Your mix has reverb tails, less upfront vocals, and more going on arrangement-wise behind the vocal, sloppier entries and exits of sounds. Not in a bad way, just that you are comparing to something that has been aligned and edited to have everything locked onto boundaries.
You should tighten up your arrangement and make all the sounds come and go on the beat if that is what you are after. Sounds artificial to me, but that may be what you are after.
Fascinating couple of links as a comparison, and a genuinely helpful response from DC-Choppah :thumbup:
Sometimes, to create music like the 'clean' 1st example, I suspect you need a 'perfect performance', because with so few mix elements and little or no reverb, the performer is totally 'exposed'.
Yes, a little clever editing may clean up such a performance a little, but often it's best to leave it as it is, even with slight imperfections, to retain the human element.
So as is often quoted here, the performance is the most important element, followed by good recorded acoustics, far more than choices of microphone or other gear in the chain.