I'm no expert, but since no one else has replied I will chime in with the differences as I perceive them... I make no claim that this is a totally accurate or complete list.
JPluckX is Java-based, the current Plucker Distiller for the Plucker Desktop is Python-based.
JPluckX handles browser cookies (read-only, it does no cookie writing but can read cookies from your regular browser) in a very simple way. Before moving to JPluckX I never figured out how to get Plucker Distiller to handle cookies, if it even does.
Most folks, myself included, seem to think that JPluckX is faster than Plucker Desktop.
As I recall Plucker Desktop gave you much greater control over the final product than JPluckX. You have more control over what links are followed and how (both have URL inclusion/exclusion lists but I seem to recall more options in PD) PD also lets you schedule commands to run before and after pluck operations.
Only JPluckX can currently generate Plucker documents for use with the new multi-image hires Plucker viewer at hires.plkr.org
I've not used the Plucker command line version included with Plucker Desktop so I can't comment on that.
I've also not used Plucker Desktop/Distiller/etc. or JPluckX under Linux/BSD/Solaris/OS X/etc. so I can't comment on that either.
I hope this has been some small help.
eponymous