You have a good question. Plants absorb nitrogen in the form of ammonia or nitrate. These are very small water soluble molecules that can easily be transported across the plant cell membrane.
Here's the MSDS for Schultz plant food; it contains urea, ammonium, potassium phosphate, and potassium nitrate and trace elements. All small molecules. http://www.schultz.com/~/media/Schultz/ ... FEB08.ashx
Organic fertilizers like blood meal, cotton meal, and manure contain proteins, which are much larger nitrogen-containing molecules. In order to use the nitrogen in organic fertilizers, the large molecules must be broken down to ammonia or nitrate by bacteria growing in the soil. This takes time, so the nitrogen is not instantly available to the plant, but it is available over a longer period of time.
Here's the MSDS for an organic fertilizer that contains fish proteins and seaweed. This is a complex source of nutrients, definitely no nitrate or ammonia. http://www.garden.com/ContentFiles/Asso ... 40MSDS.pdf
Organic fertilizers typically contain lower concentrations of nutrients. Look at the labels on the fertilizers you purchased. The first number on the label is the nitrogen content; if the non-organic fertilizer has a higher number, then it was a more concentrated source of nutrients. If your son used the same quantity of each type of fertilizer, then he probably used less nitrogen for the organically grown radishes.
Perhaps when discussing this with your son, you could explain that the non-organic fertilizer provides nutrients faster and the organic fertilizer is slower. Is faster growing better than slow growing?
Your idea of a taste test is a good idea for a future science fair project. Organically grown foods typically taste much better than regular foods, so this is a topic that is definitely worth investigating.