Just like any other country, your chances of finding work in New Zealand will depend on many factors, including the state of the economy and even the election cycle.
I think most recruitment companies or employers will look first at your job experience for a given role. If you have worked in the same or similar position previously, then your CV will get a second look, or the recruiter/HR rep will be interested enough to talk with you. If you are a recent graduate and are new to a particular field and have no prior [related] experience, then it will depend on the strength of your overall CV and supply and demand. If an employer is desperate to fill a particular vacancy - something which almost never happens in NZ in my experience (being desperate, that is) - they may be willing to consider candidates with no prior work experience. Certainly, your academic degree will count, but generally, experience trumps education almost every time.
The next thing to consider is something that most people fail to fully grasp: New Zealand is a small country. The number of potential jobs and employers is comparatively small in any field, and in some areas, even smaller due to the size of the industry in NZ. New Zealand employers are generally by-the-book, in that they will first determine if you have the right to work, before assessing you as a potential candidate. In many cases, the advertised job will be with a government entity such as a government ministry or department, or a regional or local council. Or if a private company, the employer may depend heavily on the public sector (the same government entities) for its survival. What this often means, is that advanced jobs which might require or prefer a Masters degree or formal academic education, will probably stipulate that the candidate have permanent residence or be a citizen.
Subconsciously or unofficially, there may be other biases at play when assessing job seekers, such as a preference for home-grown candidates (native New Zealanders) or a dislike for candidates from a particular country. That will vary based on the employer and recruitment agency, and this happens, I believe, in most any country. I think it is safe to say, however, that if you are in New Zealand on a work visa, you will need to have hard-to-find skills or experience to be competitive with other candidates who are established and have permanent rights to live here. However, even if you hail from an advanced nation and have the newest skill set in some technology area, don't expect New Zealand to be cutting edge. The work culture is very conservative here; kiwis generally will wait for a long time to adopt a new method or technology after the rest of the world has long since accepted and employed/deployed it. New Zealand tends to wait for the rest of the world to prove the veracity or efficacy of new ideas before slowly catching up. So, if you have dev skills in some rare javascript flavour of the month, or you just wrote your masters thesis on some innovative economic theory, you can't expect your research or skills to be in high demand here or even desirable - in fact, it may actually hurt you.