Marsh, who is also director of England's National Cricket Academy, was not prepared to back the host nation to break Australia's 16-year hold on the Ashes but said England's cricket culture was stronger than ever.
The two sides play a five-Test series starting at Lord's in July.
Marsh said Australia's strengths lay in the extraordinary talents of keeper-batsman Adam Gilchrist and the experienced McGrath and Warne.
But he warned that the complexion of the series would change if both bowlers were hit by injury.
"If you want to talk about the fundamental difference between the two teams you've just got to look at Warne and McGrath, with a thousand Test match wickets (between them), and then you go wherever you want to go," he said on Sunday.
Warne, 35, and McGrath, 34, are fit after making successful returns from long lay-offs in the past year.
But Marsh said Australia could not afford to lose the pair, as it had struggled without them in recent series.
England beat Australia in the fifth Test of the 2002-03 series, when Warne and McGrath were injured. Australia lacked firepower against India's batsmen last summer with both bowlers out.
"The question that's going to be asked of me a thousand times between now and whenever that Test series starts, is 'Who's going to win the Ashes?'," Marsh said.
He said it was impossible to predict, because if McGrath and Warne were unfit it might make a huge difference.
"If (England quick Steve) Harmison only gets nine wickets for the series or whatever, that'll make a huge difference; if (England allrounder Andrew) Flintoff's not fit, that'll make a huge difference."
Marsh, who will be inducted into the Australian Cricket Hall of Fame on Monday night, will finish in his dual English role after the Ashes series.
'It will be four years, which is amazing -- it doesn't feel like four years -- by the time I leave, and hopefully England are a better side than they were four years ago and that's the bottom line," he said.
England are now the second-ranked Test nation behind Australia. Their 2-1 win over South Africa was their fourth straight series triumph in the past year.