What would have happened if New Zealand had declined to participate in WW1?
(I realize this was never an option at the time - Pakeha of that era thought of themselves as British in much the same way as NZ expats of today regard themselves as Kiwi).
Would the outcome of the war have changed?
Probably not. WW1 was predominantly a war of numbers as opposed to quality of troops. Not having New Zealand troops would have made very little difference - unlike the USA, whose belated intervention was one of the decisive factors. It is possible that the Gallipoli landings would not have gone ahead without NZ troops - this would probably have helped the Allied cause, although some believe that the Dardenelles operation ensured that Turkish troops could not be deployed on the Western front, preventing German conquest of France.
What would have happened to New Zealand?
NZ relations with Britain would undoubtedly have suffered in the short term. However, Britain maintained friendly relationships with numerous states that were neutral in WW1 (for instance: the Netherlands, Scandinavia and Spain). Conversely, two of the WW1 allies (Italy and Japan) were on the enemy side in WW2. Britain had a primitive agricultural industry that was depleted of labour by the war and thus needed New Zealand's exports both before and after WW1 - thus making friendly relations even more imperative.
Non-alignment would however have removed the sense of NZ as an offshore province of Britain. NZ may well have followed a path similar to Eire - as a country linked by family, language and commercial ties but politically fully separated).