Whilst I agree with UMAG on the fact that it depends what your friend wants to see, I don't really agree on the strengths he lists.
First of all, scratch Australia Zoo from your list unless she's more interested in watching a small child dance than seeing animals. It costs around $60 for an adult to get in, and once there you'll find you'll see elephants, tigers, otters, red pandas, some natives and lots of crocs... and if you want to see the primates, giraffes, rhinos or cheetahs, you can expect to pay plenty more besides.
Will this person stay with you in Adelaide? If so, then a combination of Adelaide, Monarto and Cleland would see them get a taste of an excellent native animal collection (at Cleland), a very large but still developing open range zoo, and one of the best urban zoos in Australia, which of course has the giant pandas. Between these three SA zoos, you'll see all the major species Australia has to offer except elephants and gorillas.
Taronga is more 'spectacular', although I feel my home zoo, Melbourne, stacks up with better gorilla, tiger, elephant and orang-utan enclosures, a slightly better reptile house and what I believe to be the best flight aviary in Australia. Plus, the excellent chimpanzee exhibit at Taronga is currently being rebuilt. Against that, Taronga has the harbour views, an excellent seal and penguin complex, a lot more native animals (if you wished to cut Cleland from your Adelaide itinerary) and a decent number of smaller aviaries (although I believe some have been demolished since I last visited). Another advantage of a Sydney trip is you could combine it with the truly excellent Sydney Aquarium, which is the only place in the world apart from (I think) Singapore where you will see dugongs. The Melbourne Aquarium, regular visitor though I am, doesn't compare favourably.
As for Monarto versus Werribee, I can't really say as I've never been to Monarto (for that matter, my only visit to Adelaide was a fleeting one for 1.5 hours seven years ago). My impression is that Werribee has more "finish" to it than Monarto, but from what I can gather I feel sure that I would get more out of visiting Monarto. They have marginally fewer mammal species, but the fact you can get out of the bus and linger at each one - not to mention large breeding herds of many of the species - makes a big difference to me.
I don't know if any of that helps. Is this person a zoo fanatic like those of us on this website? If so, then she'd get huge value out of going to at least Taronga, Sydney Aquarium, Melbourne, Adelaide, Monarto or Werribee and one of Cleland or Healesville Sanctuary. I don't know how willing she is to go off the beaten track, but Taronga Western Plains at Dubbo is infinitely more worthy of her time and money than Australia Zoo in my honest opinion, having been to both zoos once in recent years.