I just happen to own both. I purchased the Case Slimline Trapper first and the soon followed up with the Hawthorne (clip point blade) because I was looking for better build quality/materials in the same pattern.
The Case slimline's handles are slightly slimmer (for lack of better work) than the Hawthorne due to the covers on the Hawthorne being slightly thicker and more contoured. One should note that I own the yella delrin handled/CV bladed slimline. The other bone handled versions may or may not be wider. The handle on the Hawthorne is slightly shorter than the Case, making for a higher blade:handle ratio on the Hawthorne.
The blade lengths are the same as far as I'm concerned but the blade stock is substantially thicker on Hawthorne. In my opinion, the Case cuts better due to the thinner, hollow ground blade stock versus the Hawthorne's thicker, sabre ground blade. The hawthorne is no slouch though and still outcuts pretty much all of my modern folders.
Another point of note is that the Hawthorne has a half stop whereas the Case does not.
In terms of build quality there's no real comparison. The hawthorne blows the case out of the water. The action is MUCH smoother and the blue camel bone covers are polished beautifully. Also the blade is centred perfectly on the Hawthorne, whereas my Case has a significant amount of rub.
I wish I could post some pictures comparing them both but I just gave my mother the Case yesterday because she liked it so much. It now resides in her purse.
Just a suggestion: If you've never owned a slim jack before then perhaps pick up the Case to see if you like the pattern. They can be had for a song and you can always decide to pick up a Hawthorne later.
Tyler