I think Pakistan could challenge us. When fit, they'll have a bowling attack of Asif, Gul, Akhtar, Naved, Saqlain (not gonna happen).
I think Mills & Bond will trouble our top order batsman and Vettori will chip in with a few wickets but generally I think the bowling lineup of McGrath, Lee, Johnson, Clark, Bracken, Hogg or whoever we decide to play will probably destroy New Zealand's batting lineup and end up saving us the match.
As for England, unless acouple of their batsman steps up and makes a match winning hundred then I don't see them winning a match on this tour.