What I am about to say here is based on my experience logging 4000 miles on a 2004 BD chopper before upgrading to a K9. I've logged 16,800 miles on a k9 since July 2006.
The chopper will be noticeably more nimble than the k9 with the slighty shorter wheel base and 250 rear tire.
The k9 will be more balanced than a 03 chopper because of the "slam-clutch" primary. The primary doesn't extend as far away from the bike. Some claim the early choppers pull slightly to the left because of this. I never really noticed it.
I'm 5'10 with a short 30 inch inseam (probably a 29 really). The K9 really fits me well. The handlebars on the chopper models don't extend quite as far back toward the rider as the k9 bars. On the chopper I was having to lean forward more than I would like. On short hops it didn't matter, but on a 400-500 mile day it sucked. If you are taller than I am you can probably disregard everything I just said.
You tend to sit slightly deeper into the bike on a k9 vs the chopper.
Ground clearance I believe will be .5 to 1 inch higher on the chopper compared to the k9.
As for suspension, the k9 probably absorbs bumps better due to the 300 rear tire and slightly longer wheelbase. It's not a dramatic difference.
off topic from ride quality, I personally believe the 250 rear tires last longer than the 300s on the k9. Also, the 03 chopper didn't use proprietary made for big dog parts by s and s. Engine parts for an 03 chopper could be ordered directly from s and s. If this is incorrect someone here will put me in my place.