I don't think one is better than the other in terms of performance. There are some differences though.
Flemish strings take less equipment to make. They can be done with nothing more than a measuring tape, a server, and a knife, but a jig is much handier. The jig is smaller. They also take less serving material as only the center is served.
Continuous loop strings require a more elaborate and much larger jig. They also need about twice as much serving material per string. The served loops may last longer than Flemish loops and the string requires fewer twists (just enough to make it round), which may also contribute to longer string life. I doubt that the difference is huge though. It is also easier to consistently duplicate string length with a continuous loop jig.
I make both, but lately I have been making mostly continuous loop strings. Not because they are better, but because my hands tend to cramp up when making Flemish strings. So if I want a string made painlessly, I do a continuous loop.
Personally, I think Flemish strings look nicer and may be a tad quieter, especially on a recurve bow. It really comes down to a matter of personal taste. Both are excellent strings, and when properly constructed, both will give excellent service. I use both.
You can't go wrong, no matter which you choose.
Russ