Ms Bishop said her rival behaved like a "fashion model or TV star'' while Ms Gillard labelled the Education Minister "Mistress of the Trivial Issue'''.
The comments stem from numerous magazine profiles on both women, culminating with Ms Bishop dedicating much of her most recent interview to criticising Ms Gillard, who is the Deputy Opposition leader.
"I don't think it's necessary to get dressed up in designer clothing and borrow clothing and make-up to grace the cover of magazines,'' Ms Bishop told The Sunday Telegraph.
"You're not a celebrity, you're an elected representative, you're a Member of Parliament. You're not Hollywood and I think that when people overstep that line they miss the whole point of that public role.''
However, Ms Gillard said that Ms Bishop's "inaccurate and inane'' comments reflected a Government desperate to hold on to power.
Ms Gillard said described Ms Bishop as a "silly sausage'' who should simply concentrate on her portfolio responsibilities. "It shows just how low this Government has sunk in its bid to hold onto power,'' Kevin Rudd's deputy said.
Ms Gillard recently appeared on the front cover of The Australian Weekend Magazine and the ABC's Life Etc magazine.
She has also appeared on Australian Story and posed for the cameras with her partner Tim Mathieson.
She defended the magazine interviews as a "very legitimate thing for a politician to be doing'' and said Bishop had recently done a similar interview herself with the Australian Financial Review magazine.
"This just goes to show she is Mistress of the Trivial Issue,'' Ms Gillard said.
Ms Bishop said The Australian Weekend Magazine shoot, in which Ms Gillard posed in designer clothes and pearls, was "her Cheryl Kernot moment''.
She was referring to an infamous spread posed for The Australian Women's Weekly in which the former Labor MP mously sported a red feather boa and satin dress.
"Why would you go along and do a fashion shoot as Julia Gillard did the other day, with clothes by Carla Zampatti, jewellery by ... hair by ... ?'' Ms Bishop said. "That's not what it's all about.''
Ms Gillard said image was not important to her, but she believed the public had a legitimate interest in the lives of politicians.
She denied she had exploited her personal life for political gain. "There are parts of my life that are very private, that I certainly don't reveal ... but The Australian interview was quintessentially about politics,'' Ms Gillard said.
She said Ms Bishop's comments were "inaccurate in the impression she's trying to give of what I've done, and inane in that it's not the sort of thing that matters to Australian voters.
"They want to know what's happening with their education system, with their health system, with their industrial relations system. They're the sort of thing that matters to them, not this sort of distraction.''
Ms Bishop said posing for magazine covers was "not my style''.
"Of course people want to know more about you but I don't think you should be courting that celebrity status as if you're a fashion model or a TV star because you're not,'' she said.
"I have nothing to hide but I don't promote my personal life as a reason for people to vote for me.''
Originally published as It's Julie vs Julia