Split fins are a relatively recent invention, developed in the late 90's. They are easily recognizable as fins that are, well, split down the middle. Before we get into them, let's talk about basic fin design.
The purpose of fins is to convert the up-and-down motion of a kick into forward thrust through the water. The more efficiently it does this, the less energy it requires for you to move, since a higher percentage of kicking energy is converted into thrust. This efficiency is generally what makes one fin considered "better" than another.
Most full fin designs have some sort of ribs on the edges and possibly in the middle, creating channels along the fin. This directs water along the fin, ensuring that most of it gets pushed backwards, in turn pushing you forward. The ribs prevent water from "spilling over" the edges of the fin.
This is straight-forward, but things start getting fancy with split fins. Split fins are in principle similar to a propeller, which uses hydrodynamic concepts to turn rotational motion into forward motion (i.e., the blades spin and the plane / boat moves). As you kick, the fins angle inward, forcing water down a narrow channel. This creates a pressure differential that, along with the water running down the channel, helps propel you forward. (Note to physics geeks: see Bernoulli's Principle)
Ok, sure, but what does it mean? Basically, that you get more motion for the same amount of kick. Split fins are more efficient and thus, "better" by some definition.
It's not all good, though. This description only applies for the usual flutter-style kick. If you are a frog kicker, split fins will actually be less efficient than ordinary full fins. For this reason you won't see split fins on a lot of wreck or cave divers.
Split fins are also expensive, costing 2-3 more than regular fins. It's up to you, whether the extra cost is worth the increased kicking efficiency. Besides, fins are probably not the most expensive piece of scuba equipment you'll buy (even split fins), so when you factor in their lifespan, the extra cost becomes less significant.
I use these split fins from Apollo. Although I haven't had much experience with other fins, I really enjoy them.
In the end it comes down to the importance you place on kicking ease and your budget. However, next time you shop for fins, at least check them out and see if they work for you.