Split fins put less strain on ankle and knee joints. For divers with joint issues or who get frequent cramps in their legs from exertion, they are a good choice since they give these divers useful equipment to keep them diving comfortably.
Swimming with splits is quite effective for flutter kicks, but because it's nearly impossible to use them to swim backwards, "elite" divers like cave and wreck penetration divers find them a hindrance for the kind of diving they do, which may involve some backing up. Paddles give these divers the equipment they need to keep them diving safely.
Because flutter kicks tend to stir up sediment when the diver is close to the bottom, many proficient divers (and those who dive in silty places like the interiors of wrecks and in caves) prefer frog kicks. Splits are designed for flutters, so they are not as efficient as paddles for frog kicking. I bought a pair of splits years ago when I was first buying gear and did a huge amount of diving with them since they are very comfortable. I learned to do frogs and heli-turns and can generally maneuver very well in splits, with the notable exception of swimming backwards, but many divers who have learned those techniques in paddles just can't make them work in splits, so why switch? They are fully justified in sticking with what works for them--paddles.
I still dive both styles of fins, but I don't subscribe to the elitist put-downs of splits. They are perfectly fine fins for casual diving and great fins for those divers who have leg issues.