Hi,
My first thought reading your post was that you are not being offered a great deal at all, but given the feedback from others realise that we must have been very very lucky indeed as the company I work for paid for nearly everything, including accommodation on arrival for a few months.
The only thing we had to pay for, in terms of relocation, was to bring our dog and cat over. Oh, they also didn't pay for the visa applications, medicals and police checks but that was small in comparison to flights and shipping.
I agree about the Middle East, having worked there as well and I wouldn't generally expect the same expat deal as you possibly got there.
I would suggest trying to negotiate at least your flights and some shipping costs, but as Manks has highlighted the economic climate has changed in NZ quite a lot in recent years.
Worth a try though.
PM me if you want any more info.
Good luck