These act like their synthetic counterparts in that they kill insects indiscriminately and upset the balance of pests and predators that you're trying to establish in the garden. A lot of organic gardeners don't use these at all. If you're desperate and feel you must use a spray, these chemicals can be kinder on the environment. For instance, neem oil has been used for centuries as a toothpaste in India. However, nicotine is a neurotoxin, and can be dangerous.
Rotenone can kill fish.
If you do choose to use these sprays, bear in mind that you will also kill any beneficial insects you have. Then you will need to wait for your beneficial population to recover.