Hi Becker,
Firstly the new Party Wall ought to be built as high as the Approved Planning drawings. If the works are being undertaken under Permitted Development, then presumably you may have already applied for a Certificate of Lawfulness from the local council. The council will have checked that the wall heights to make sure they do not exceed the Permitted Development Allowances. Typically this is a wall which starts at a max. height of 4 m and slopes down to the 'Eaves' which have a maximum height of 3 m. That said Permitted development does not stipulate or make allowance for a roof parapits, worth reading up on. The roof parapit, if you have one, can extend up further.
All this said, when you served your Party Wall Notice to your adjacent neighbour, if they 'consented to the principle of your works' , they would have been agreeing to the information contained in your supplied drawings. If they did not accept the principle of the works and instead elected to have a Party Wall Award put in place then these details should have been interogated and agreed, prior to works starting on site, by the Appointed Party Wall Surveyor. You mention the Adjacent owner having an Architect? If that Architect is a qualified Party Wall Surveyor that's fine- otherwise he does not fit the role of Adjacent owners appointed Party Wall Surveyor which is stipulated by the Party Wall Act 1996.
I hope this helps.
Best Wishes Lee Davidson Dip Arch RIBA