My brother exchanged his NZ licence and received a UK licence that only allows him to ride a tricycle. I had an identical licence and exchanged mine for a full UK bike licence. Apart from having to resit his tests and get a UK bike licence what else can he do? To me this is a simple clerical error that DVLA should correct.
This UK govt page discusses exchanging a drivers licence obtained overseas for a UK license. Because NZ is a "designated country," the page says the NZ license can be transferred.
Because a driver's license for a car will only exchange for a UK driver's license for car, and the same for motorcycles, I infer that an applicant's driving privileges can't be changed in the exchange. You've said both of you had the same type of NZ licenses, allowing unrestricted motorcycle use.
I assume you both filled out DVLA's form D-1; the form, unfortunately, is not available for download so I cannot see it. I'd expect it to require the applicant to specify the type of license for which exchange is sought.
If the D-1 form asked that information, and you both provided it, then I agree that DVLA erred because the results weren't the same. Because I don't know the actual underlying UK law...it's possible that DVLA erred as to your license and took the correct action with his.
I think the three courses of possible action are: 1) have your brother go to DVLA and raise the issue with them; 2) do nothing, with your brother starting the motorcycle licensing procedure anew if he wishes; or 3) consult with a solicitor who knows about UK driver's licenses.
I'm a retired attorney in the US, and always wanting to know the answer (i.e., in which case did DVLA err?) before I engage, favor alternative #3. With easier access to UK law, and knowing how to look it up, this shouldn't pose a significant challenge for a legal practitioner.