Recurves are simpler in design and simpler to maintain, have fewer things to go wrong and have no cables to replace or reserve. But they tend to be wider than compound bows.
Compound bows rely on both limbs and pulleys to generate thrust. As a result, the fastest bows are compound. They are generally narrower, but not necessarily lighter.
Both types of bows can be quite accurate. I think it's more a matter of personal choice and own representatives of each kinds.