Well, the two games that England won in the NatWest series included one where Symonds and Lee were both missing. That left an attack of McGrath, Gillespie, Kasprowicz, Hogg and Watson, and Gillespie and Kasprowicz were obviously woefully out of form or past it or whatever. Certianly not comparable to the strength of the Australian bowling attacks that NZ has usually faced in ODIs, excluding last year with Lewis, White etc.
Anyway, if England aren't at full strength because they don't have Jones or Trescothick, surely Australia missing Symonds and Lee is equivalent given that they are much, much better ODI players, even leaving aside form issues.
I'd offer more examples, but you're really basing your entire argument off 2 or 3 matches, so there's not so many examples to work with. Suffice to say that aside from that one tour there's no evidence that England handle playing Australia in ODIs any better than anyone else. England lost a match last world cup from a winning position against Australia, and until that CT game they'd lost 12 ODIs in a row or something against Australia. Since then they've won 2 games and lost 3 in a home series and been comfortably beaten in a match last week. That record isn't any better than New Zealand's over the same time frame.
edit: Just checked. Since that 01/02 VB Series that New Zealand did well in, Australia and England have played 16 times in ODIs, for 11 wins for Australia, 3 wins for England, a tie and a no-result. That includes 6 consecutive wins for Australia in the 02/03 VB Series, one World Cup match, the CT semi-final which England won, the Natwest Trophy and Challenge in England last year, and the CT group match last week.