One idea could be that the crew of the Enterprise discovers a distress signal from a Star Blazers ship. They then team up to fight a common enemy, like an alien race that is threatening both their galaxies. The different technologies and cultures would create an interesting dynamic.
Faith and Seven of Nine. Faith is a complex and often rebellious character, while Seven of Nine has her own journey of rediscovering her humanity. They could bond over their experiences of being different from the norm in their respective universes. Faith could show Seven how to embrace her more wild side, while Seven could teach Faith about the importance of self - discipline and the value of technology in combat.
Captain Avatar from Star Blazers is always an interesting character to feature. His leadership skills and determination can be put to the test in crossovers. For example, if he's in a crossover with a more chaotic or morally ambiguous universe, how would he lead his crew? Another is Desslok. His complex character, being an enemy but also having his own sense of honor, can create great drama in crossovers. He could form an uneasy alliance in a crossover scenario.
One interesting idea is the combination of Star Wars' Force with Star Trek's technology. Imagine Jedi using their Force abilities to interact with Star Trek's advanced consoles or warp drives. Another is the meeting of iconic characters like Luke Skywalker and Captain Kirk. They could learn from each other's leadership styles and approaches to conflict. Also, the different species from both universes coming together, such as Wookies and Vulcans, and how they'd interact culturally.
Well, in some fanfiction, there are crossovers that involve character swaps. For example, Captain Kirk finding himself in the Star Wars universe and having to navigate the politics and power struggles there. He might use his charm and quick - thinking from the Trek universe to make an impact. Another concept could be the Jedi and Vulcans sharing their knowledge of the Force and logic respectively. The Jedi could learn about strict emotional control from the Vulcans, while the Vulcans might be intrigued by the concept of the Force.
The most interesting element is seeing the technology clash. The warp drives from Star Trek and the hyperdrives from Star Wars are both means of fast travel, but seeing how they interact in a crossover is fascinating.
One interesting concept could be the interaction between the Federation in Star Trek and the Galactic Republic in Star Wars. For example, how would their different forms of government and ideologies clash or cooperate? Another concept might be the use of technology. Star Trek has the transporter and Star Wars has the hyperdrive. How would characters from each universe react to the other's technology? Also, the idea of Jedi and Vulcans interacting due to their shared emphasis on mental discipline is really cool.