I've read a respectable amount of the arguments, and -- speaking only from a literary perspective -- there are three major contenders for the title. The first credits Mary Shelley (1797-1851) with 'inventing Science Fiction,' and -- for all intents and purposes -- it's one I struggle with the most because I think the author (while visionary, true) was chiefly tinkering with the idea of Godhood housed in man. This would make it more Fantasy than SciFi, but I've been assured that's a small quibble. The second theory is that H.G. Wells (1866-1946) deserves the credit for inspiring a generation of writers to follow in his footsteps. I've certainly no complaint with this ... suffice it to say that Wells was also famous for sprinkling a fair amount of political shenanigans in with his prose, and I, as a reader, tend to tune those things out. And the last name given credit? That would be Jules Verne (1828-1905).
For the sake of argument, I think we can suggest that Verne and Wells clearly are more nuanced contenders for the title simply based upon their respective bodies of work. One aspect of Verne that also weighs the scales a bit more heavily on his side is that, according to Wikipedia.org, he retains the title of being the most translated French-language author in the entire world ... and that certainly has to count for something?
Several of Verne's works have been adapted not once, not twice, but several times for both the silver screen and the small screen. Books like The Mysterious Island, Journey To The Center Of The Earth, and Twenty Thousand Leagues Under The Seas continue to inspire readers and like-minded storytellers to consider the unknown as places fertile for visit; and I suspect the author's library of work will be around for many decades more.