it is important to consider the chemical toxicological information of a given chemical before using it; even Neem Oil has it's draw backs so, be sure to read the Sticky on Neem Oil in the General Forum before making your decision.
Plants often secrete what are called "Secondary Metabolites" in very small quantities to ward off pests of all shapes and forms. But, when we mass produce these chemicals and use large amounts of them, they become a problem.
Even Neem Oil has it's drawbacks especialy on North Americas Bee Population which, has enough problems right now. If you do choose to use Neem Oil, please only use once a week at the most.
Oh, and given that Pyrethrins are synthesized by a plant, they are almost surely "organic" in the chemical sense of the word; meaning that they are made of a carbon backbone however, this does not make a chemical safe and organic in the sense of organic gardening. Many chemically organic compounds are highly toxic and not to mention carcinogenic.
Anyway, just some more information for you.