I own both, and there are excellent examples of both.
Here are the key differences as I see them.
1) Split fins flutter kick with much, much less resistance. It almost feels like you're not wearing fins. However, you do have to increase your cadence as you don't move as far with each kick cycle.
2) Paddle fins frog kick much better.
3) Paddle fins provide more instant acceleration. Both types of fins will eventually get you moving at about the same speed, but when you kick hard and fast with paddle fins they give you an instant burst of speed that splits can't match.
4) Paddle fins are better at helicopter turns. I wouldn't let this sway me though. Both types are more than adequate and you shouldn't have any problem doing helicopter turns with splits, paddles just do it faster and easier.
5) I find split fins seem to move me significantly better when swimming on my back on the surface. For those long surface swims I think they're a better choice.
6) They both fight current just fine.
As far as silting things up goes, I think paddle fins are slightly better, but 90% of this is a matter of technique. If you bend your knees 90 degrees and then kick using primarily your feet, lower legs and ankles you can do either a flutter kick or a frog kick that minimizes silt. Otherwise, I think a standard frogkick tends to produce less silt than a standard flutter kick, and for that reason, I would give the paddles an edge.
The other thing to keep in mind is that the fins really excel at two different types of kicks. Split fins are just hands down better for flutter kicks and paddle fins are hands down better at frog kicks. So don't try to force them to be what they're not. If you do, you'll be disappointed in their performance. Compared to paddles, split fins will feel like you've got floppy ribbons on your feet that don't get you anywhere when you frogkick with them. Compared to splits, paddles will feel like you're really straining your leg muscles when you flutter kick, while doing the same kicks with splits would seem almost effortless.