Phillip,
I tow with the current SWB Shogun, albiet a GDI, not the diesel. I have also towed with the Mk3 Shogun SWB and had a LWB Trooper for about 18 months so feel qualified to answer your question.
Firstly, the late model Shoguns are so "car like" to drive and are vastly superior to the "chassis type" of 4x4's as to be almost a pointless comparisom, at least far as a tow car is concerned, note, I am not talking about off road prowess here, which is a different subject.
Secondly , on pitching, the Mk3 did pitch quite a bit on poor surfaces and the Trooper markedly less. However, the current SWB displays hardly any pitch and is just in a different class - thoroughly comfortable and hardly ever getting upset by road conditions at all - the LWB is probably marginally better but you would have to do a back to back test to decide I think.
The SWB is more compact, slightly more economic due to less weight and is more nimble.
If you don't need the space or the weight then the SWB is OK.( the SWB is still circa 2t kerbwieght and will pull 2.8t)
the SWB takes two of us and a large dog and uncoupled has almost sports car performance. Go for it!