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I think it's actually a pretty interesting comparison.
1. Grant Fox - the perfect winner. Holds world record for points in a World Cup. Probably the best pure goal kicker of the three considering the ball technology of the time. Shocking runner, poor tackler, but he was more than just a goalkicker. His tactical kicking was off the charts, he had the best bomb of the three, and his option-taking was superb. It wasn't by chance that his outsides (e.g. Kirwan, Stanley, Tuigamala) scored a shedload of tries. Also played in a period where, in general, the game was a little more low-scoring. Most important of all, brought the ABs back whenever they were down, which I rank VERY highly.
2. Andrew Mehrtens - a perfect bridge between Fox and Carter. Useful runner but atrocious tackler. Very good kicker both tactical and goal. Possibly the best passer of the three and possibly even the best option taker. He was the first five during the golden age of ABs try scoring, and it was his passing that enabled Cullen, Wilson, and Lomu to score so many tries. Remember, he didn't have great distributing midfield backs for a lot of that period. Masterminded the greatest AB performance of the past 20 years, the 43-6 pasting of the Wallabies at Athletic Park in 1996.
3. Dan Carter - the most athletically gifted of the three by a long shot. Great runner, great tackler, booming punts, top notch goalkicking. Not the same mentally, and doesn't take over games in the same way as Fox or Mehrtens. Doesn't show bottle bringing back the team from a losing position (then again, Mehrts also failed when it counted in that regard.) It's interesting that players like Joe Rokocoko saw their scoring rate dip dramatically when Carter took over from Carlos Spencer. I don't think his passing is that good and his option taking is usually not optimum.
In my view... it comes down to Mehrtens vs. Fox. I think Mehrtens has a tiny, tiny edge in measurables, but I think Fox's world cup trophy tilts the balance and makes him the greatest first five of ABs history, and thus of all rugby of all time.
Remember: athletes aren't necessarily the best sportsmen.