Do you mean actual species, or just different colors and tail types?
If it's species, than Splendens is wanted for the long/flashy fins that they can grow. And because of this they are everywhere. The other species are almost like a novelty, especially depending on where you live (I never see anything but splendens locally). Some people might like to get one of these species just for something different. And all the species have there own quirks that make them nice; like the color of the emerald betta, or having a mouth brooding betta.
If it's the color/tail shape, then they are wanted more many different reasons. A lot of people like the less common tail types (especially true half moons, which I've heard are hard to breed for), whether for the novelty or the look it self. And many people are interested in finding a betta of a particular color, and will try hard to find what they want. Also some colors are hard to breed for, so that adds to the novelty of some bettas.
Did you have any specific species in mind?