Ultimately, they're very similar. They're both amphetamines, so as a rule, should have very similar effects. There are some differences that may be significant, depending on your son's personal chemistry.
Adderall is mixed amphetamine salts. It consists of approximately 75% dextroamphetamine, and 25% levoamphetamine. These two enantiomers are chemically identical, but physically are mirror images of one another, one formed in what they call a right twist (thus dextro-) the other a left twist (levo-). Because they are physically different, they will result in slightly different effects, the result of binding differently with the various receptors on the cells of your body. The levoamphetamine is often blamed for some of the side effects experienced with Adderall, though I believe it does promote some different positive effects as well.
Vyvanse does not contain levoamphetamine. It is made up of dextroamphetamine bound with the amino acid L-lysine. These two are split in the gastrointestinal tract, thereby supplying the body with dextroamphetamine, though ideally at a graduated pace, rather than all at once. This effect is similar to the extended release versions of Adderall. This limited release formula is intended to deter abuse, as it's more difficult to get high using this drug.
Ultimately, it's impossible to predict how your son will respond to Adderall, as compared to Vyvanse. There are many who feel that Adderall is the only option for them, and do not respond as well to medications made up of only dextroamphetamine. On the other hand, many feel that the levoamphetamine in Adderall causes increased anxiety and negative physical responses (tremors, racing heartbeat, etc). Ultimately, it's all subjective and depends heavily on one's own individual chemical makeup. If the pharmacy is being difficult, you may decide to give Adderall a try, and see how your son responds, or you may enquire about Dexedrine if they're concerned about cost. Dexedrine is one of the oldest ADHD treatment medications and is made up exclusively of dextroamphetamine, it's just not bound with L-lysine. Funny how we can re-patent an old medication by adding an amino acid, no? You probably won't have a lot of luck obtaining Dexedrine, it tends to be frowned upon in the U.S. right now, but if the pharmacy is really concerned about the cost of the patented drug, tell them they can get the same thing for cheap with Dex.
I hope you feel better informed now, despite the convoluted ramble above.
Best of luck!