Aotearoa / New Zealand

We're currently shopping around for some Insurance (House & Contents), and are trying to decide going direct with someone like ANZ (Underwritten by Vero), or using a Broker (Have received some quotes by Rothsbury, as they seemed to be quite widely recommended).

I'm finding prices similar, but ANZ definitely seems cheaper overall.

I had heard that getting insurance through a broker is better, as come time to put through a claim, they will help you through the process, and get paid out faster. Is this really the case?, and so making it worth the higher costs (few hundred more).