Heh nope, England have been just wildly erratic. On a good day England could beat anyone when it meant something. New Zealand on the other hand have been a consistently mediocre outfit, which will get you consistently to the quarter/semi finals and consistently not win anything worthwhile.
Unlike certain other sides, like for instance Australia, there's no real rivalry with New Zealand. They're too insignificant. You seem keen to try and build one up because you know Australia will crush you whenever they feel like it.