Also, I think time travel has always been more deterministic than fatalistic, if that clarifies anything at all. An example I've used before is "Yesterday's Enterprise" where it's deterministic because Worf and Troi weren't on the Enterprise, which made sense. But if it were more guided by fate (which often has no clear cause and effect relationship) they would have still been there. This is just how the circumstances of this movie appear to me.
EDIT: The mirror universe is definitely one of fate, at least in its continuation on DS9.
Sure they were influenced by the movies they grew up with. However those movies were also influenced by Star Trek. I see this as more full circle. The Cantina scene was influenced by Journey to Babel and the bar scene in TSFS was influenced by the Cantina scene. People who worked on TMP wound up at ILM and ILM did much of the Star Trek movies and television shows. Everyone who worked on Star Wars were also Star Trek fans.
Those are all things on the superficial level though. There had often been a clear difference between the two on a non-superficial level that just doesn't exist as much anymore.