I am a young adult who doesn't have any children and so can't answer your question directly about my personal experience with score difference between WASI and WISC. However, I know about the WASI and WISC. As you probably know, WASI is an abbreviated version of WISC and contains only four subtests: Vocabulary, Similarities, Matrix Reasoning and Block Design. WISC contains these four subtests plus an additional six. It is just my guess that the four subtests of the WASI are the ones the gifted do the highest on from the entire WISC since they are primarily the reasoning ones.
However, there is a possibility that your son would get a higher score on the complete WISC as opposed to WASI. Perhaps he is the kid with a stronger Working Memory and Processing Speed, which is not usually the norm for most, but you never know. Another reason the WISC might score higher than the WASI is perhaps they make the 4 subtests of the WASI harder than these same 4 subtests on the WISC in order to compensate for the limited scope and the reasoning bend of the shortened version. Finally, (and I might be giving you false information on this so you have to check) it may be that there is only one version of the WASI which is given to both children and adults, meaning the same WASI is given to both children and adults. Although in that case the scoring would be age adjusted, but the items themselves would be harder since they are meant for adults. WISC, on the other hand, is specifically designed for children so it may be easier.
So, I told you all I know. I know personal experience would be more telling, but I hope I was helpful. And hope you can plod through my rambling.