Personally, I lean towards Sci-Fi as well, though I do think that fantasy is more likely to lean towards the spiritual side. It's easier in a Fantasy story to have a moment where "God" influences events, and where his plan moves forward. Why do you think there's so much Christian Fantasy?!?!? Also, fantasy brings out a more allegorical side to the story, allowing for a more supernatural side to appear.
Science fiction , often concentrates on the more naturalistic side of reality, including how societies develop, ethical choices, and the existence of unnatural phenomena. Now, both could explore spiritual elements. Look at the work of Arthur C. Clarke (2001: A Space Odyssey, Childhood's End). His stories often have New Age endings with characters "Ascending" into whatever the spiritual reality of the story is. The stories reek of a New Age vibe ,and make me want to never read his stuff ever again. But this only worked within the New Age perspective.
Most Sci-fi sticks to a naturalistic worldview, which sees the physical world as all there is. They don't attempt to seek out the nature of reality. That can be problematic. But I've found many a science fiction book to engage subjects of lasting importance fairly well.