Thought about doing this as a poll, but I think it needs more than that. There is no doubt that science fiction has a way of inspiring real life tech over time. As long as we can agree with this assumption, then we can lay out how effective these two scifi narratives are at shaping our actual future.
For example, I would attribute the modern cell phone and portable computing devices to Trek, while I would point to modern robotics breakthroughs to Star Wars.
There are many more I could list on both sides, but I am much more interested in what you have to say about this. Keep in mind, this is not a “SW is better than ST” or the other way around, it is strictly an issue of which has inspired more usable tech.
My own opinion? Advantage Trek.