I'm really amazed at the number of people who've not played New Zealand Story. I considered it one of those games that everyone has played, like Out Run or Golden Axe.
You might be surprised, but the NES release of Kiwi Kraze was the ONLY console version of NZS to come to North America. Of course, there were C-64 and Amiga versions, but again consoles ruled the roost. Typically if I see a game like NZS or Rainbow Islands on a person's "best games ever" list, I can peg them as a Brit from a mile away.
The convenience store near my Jr. High school had NZS and Rastan Saga II, which is where I first learnt about both games, and I bet most people in the US or Canada remember NZS in the arcades first, and perhaps as an import second.
It's also easy to answer why NES Kiwi Kraze is more fun than the PCE version: the PCE NZS has sub-NES music quality.