Well, someone stop me if I get anything wrong here:
Big Trouble in Little China started out as a western. Eventually the original writers were taken off the project and Richter (director of Buckaroo Banzai) was brought in while he was still working on BB vs. the World Crime League. Production for BB vs. WCL broke down, repeatedly shot down by its producer, who was terrified that the paperwork for a sequel would expose his embezzling.
Richter’s new script for BTILC obliterated pretty much everything in the original BTILC script (notice how … well, for one thing, it’s not set in the wild west?). As a result some creative souls put two and two together and determined that BTILC was, in fact, the sequel to Buckaroo Banzai.
While Richter might have cribbed a few ideas from BB (and certainly the overall “feel” of the works are similar), the rumor has been denied:
This rumor crops up more often than the scuba diver in the forest fire. While “Big Trouble” is a favorite around here, it is its own film from beginning to end. It’s no surprise that it has the flavor of one of our adventures since the final screenplay was written by our favorite docudrama producer/director W.D. Richter. According to Mr. Richter, screenwriters Gary Goldman and David Weinstein created the original screenplay as a western. Director John Carpenter asked W.D. Richter to modernize it as a way of simplifying an already complex story. While this may seem a bit odd, it does explain why Jack Burton rides into the sunset on his horse (now a semi truck) instead of kissing the girl.
That said, BTILC does seem to me to be a “spiritual sequel” to BB.