I would rate it higher than most people because their single biggest strength is the cat and carnivore collection, and I am a cat fanatic. So for me personally it is my favorite California zoo. Objectively speaking, on general grounds, it is still quite good but obviously not in the same league as San Diego. I like it better than Los Angeles, but I have not been since the latter opened their new elephant and reptile exhibits, plus of course their upcoming South America exhibit. I have not been to zoos in other parts of California (except Santa Barbara), so I cannot really say.
It is an excellent zoo, and an even better botanical garden. They still have a few old cages and the reptile house is a bit small, but most of the enclosures are really good. There are great collections of African and North American desert animals.
I've been to 20 of the 24 AZA-accredited zoos/aquariums in California and I'd rank The Living Desert in the #3 slot just behind the two huge San Diego juggernauts. For the most part the exhibits are of a very high quality and the desert atmosphere adds to the environment. I will add that I last visited Los Angeles Zoo in 2008 and so since then there has been some worthy additions (Elephants of Asia, LAIR Reptile House, upcoming Rainforest of the Americas) and thus L.A. is much improved these days.
Along with ROA, LA will soon be reopening the former Koala House and renaming it the Australia House; to exhibit Sugar Gliders, Echidnas, Bettongs and Wombat. As for the Living Desert, I would rank it amongst the top 5 California Zoos I've visited; behind San Diego, San Diego Safari Park, and Los Angeles. After The Living Desert I would rank Santa Barbara, San Francisco, Sacramento and Santa Ana in about that order. I've never visited the zoos in Oakland or Fresno, though I have been to both cities. Maybe sometime soon. They're desert habitats are very well done, though very much rivaled by Phoenix; I've yet to visit the two institutions in the Tucson area. I would not recommend visiting anytime after June, or before November however, due to extreme desert heat.