Rudd, a former foreign minister and diplomat in Beijing, accused Abbott of trivializing the Syrian regime's use of chemical weapons against its own population.
"The last time I used the term 'goodies and baddies' was when I was playing cowboys and Indians in the backyard," Rudd said. "I think I stopped doing that about the age of 10."
Abbott a former Roman Catholic seminarian, Rhodes scholar and journalist rejected the criticism.
"The odd use of colloquialism is perfectly appropriate if you are trying to explain to the public exactly what the situation is," Abbott said.
The comments come as an opinion poll published in The Australian newspaper on Monday showed Abbott's conservative coalition holding a large lead over the ruling center-left Labor Party, with 54 percent of voter support compared to 46 percent.
That result could deliver Abbott's coalition close to 90 seats in the 150-seat House of Representatives, where parties need a majority to form government, Newspoll chief executive Martin O'Shannessy said.
The poll by Sydney-based market researcher Newspoll found that Abbott has for the first time overtaken Rudd as preferred prime minister, 43 percent to 41. The other 16 percent of respondents were undecided.
The poll was based on a nationwide random telephone survey of 1,116 voters at the weekend. It had a 3 percentage point margin of error.
The government has accused the opposition of putting too low priority on Australia's international relations.
Abbott told the National Press Club on Monday that if elected prime minister, he might not attend the next sitting of the U.N. General Assembly in late September if he has domestic demands.
Rudd backed a campaign that delivered Australia a temporary seat on the United Nations Security Council. This week Australia accepted the rotating monthlong presidency of the Security Council.