The advantage of split fins (according to the ad-blurb, anyway) is that they allow a much shorter, more streamlined flutter-kick than non-split fins, which reduces swimming effort, and hence air consumption. They are also supposed to be better for surface swimming, since they produce less 'splash' (and hence waste less energy) when breaking the surface
As a full-time instructor I used non-split fins (Mares Avanti Quattros) for almost my entire working life (2000-2005) and have since continued to do so on fun-dives. I have only once used split-fins (Scubapro TwinJet, borrowed from a colleague to try them out) and I didn't get on with them a-tall, likely because I was thoroughly habituated to my own fins.
I found that particular model too floppy, and almost totally ineffective when doing 'frog-kick' (like most instructors I know, I hardly ever use the 'traditional' flutter-kick). I had no confidence that they could provide me the power and manouevrability that I might require in an emergency--but perhaps if I had taken a little more time to get used to them, I would have got to like them better.
I would however emphasise that I do not have any experience with other models of split-fin, so my comparison is not only extremely limited, but also highly subjective. Someone who buys split-fins early in their diving career, and uses them habitually will likely have a different take on things.