A pulley rig is designed primarily for fishing over foul ground, where snags are a likely problem. When you hook a fish that exceeds the weight of the lead being used, it will help the lead lift over the snags, thereby return to shore and clear any likely problems. Most will admit it can be a pain to carry spares, this because they tangle easily in the tackle bag. I have overcome that problem very easily and if you send me a PM I will send you a picture of an excellent cure.
The running trace is a rig of pure simplicity. It is easy to make, simplicity to rig, and you can simply keep spares in a small ziplock bag. You also have the additional benefit of tying the trace to whatever length you wish, sometimes long, most times reasonably short.
The flapper rig is more for fishing off a wharf and is very popular with beginners. YEM's and small bait fish are usually the target, not really recommended for the surf.
From your question regarding losing fish on the strike I believe the answer is simple: you are striking too soon. If I get a take, regardless of how strong, I will hold the rod and wait for the fish to return to finish its meal. Of course this is not the case if the fish is still pulling line. It is quite amazing the number of times I have heard an angler bemoan, "How could I miss a take as strong as that?" Well it's really quite simple, the fish had taken the bait, not the hook.
Sometimes the wait can be quite some time, I put the rod back in rest but don't stray far from it, the return may take a few minutes. When I fished the Bay of Plenty beaches I quickly learnt the best way to miss a snapper was to strike the first bite. One evening out of exasperation I put the rod back in the rest and muttered to the fish, "Bloodywell get on with it", strangely a hook up followed - I learned my lesson well.
I have been following the advice of a top match angler. He states quite simply, if he gets a bite he will turn his back on the rod and go and pour a cup of tea. The result being as many fish are creatures that shoal, he winds in two fish not one. This is more for smaller fish but I can see it working quite well when gurnard reappear on our beaches.
One rig I am looking forward to trying is the pulley wishbone rig. I already have some of these tied and I can't wait to give them a run. If I get a session or two in before I go to China I will put a report on here.
I hope all this helps.
383