For me personally, I like the soap for soft bodied pests or at first sign of spider mite infestation. I spray in the morning and there is no harm to bees once it has dried. After a couple applications spread about 4 days apart, I then spray down the trees with water and it comes off easily. I have not noticed any harm with real insecticidal soap.
Neem oil I primarily use when my deciduous trees are bare. I give them a good spray for their light anti-fungal properties and kill off any possible dormant pests. I also use it on heavy spider mite infestation as it disrupts the reproduction of insects as well. I find it to be a little more "harsh" on the plants than the insecticidal soap. Also, neem can interfere with the bees reproduction so it is advised you do not spray it around a plant in flower.
I really try not to spray my plants with anything, though. Since both these products work by suffocation, they kill beneficial insects as well. Right now, as my citrus trees are growing rapidly, the aphids are attacking the tender growth. I'm choosing not to spray them since I am noticing many lacewing eggs and larvae on the trees. They will naturally get everything in check. If I were to spray, I'd be killing the beneficial insects as well.
