For what purpose?

Beyond that, both require direct hits. thus neither is preventive.

I don't know, but something is chewing at the leaves of my squashes. I left some slug bait out just in case.

But just out of curiousity, why would someone choose insecticidal soap over pyrethrin or visa versa, or do they work the same?

In the Integrated Pest Management scheme of things you always start any control program with the least toxic material available and since any pyrethrin based product is a very broad spectrum and quite toxic substance that should be about the last thing used.
First you need to identify what is the problem so the appropriate control can be used. For any Insecticidal soap to work you need to see and directly spray what is causing the damage since Insecticidal Soap has no residual affects. Second, you need to decide if any damage being done actually needs some control, or is that so little that nothing (very often the best means of control) needs to be done. Third, if you decide a control needs to be used then you need to identify the appropriate, least toxic, method of control. Fourth, you need to apply that control. And last review what you did and determine if that was effective of not and if necessary go back to step one.

I've used products designed to reduce moisture transpiration from plants such as, Vapor-Gard and Wilt-Pruf as an insect control in the past because it puts the insect in a 'cement overcoat' preventing movement and feeding. Caterpillars can only breathe if they can move..no lungs..so preventing movement can kill them. Tiny aphids with microscopic legs and joints can't move once the material dries on them, and as a by-product...I've reduced moisture evaporation off the plant leave surface, the product's intended purpose, so nothing is wasted. In IPM it's often necessary to attack the insect through it's own vulnerabilities and where size, movement and the need to breathe are only a few of those 'requirements'.

An improper use of a product is not acceptable to an organic gardner/farmer.

An improper use of a product is not acceptable to an organic gardner/farmer.

Since when? Most organic gardening solutions come from people improvising. Baking soda or milk for powdery mildew, for example.

For those interested:

http://en.wikipedia.org/wiki/Pyrethrin

"The pyrethrins are a pair of natural organic compounds that have potent insecticidal activity. Pyrethrin I and pyrethrin II are structurally..."

"...The pyrethrins are contained in the seed cases of the perennial plant pyrethrum (Chrysanthemum cinerariaefolium), which is grown commercially to supply the insecticide."