I've been to the Moscow Zoo twice, including just a couple years ago. On both of my visits, I very much enjoyed my time there. I was not expecting a super modern zoo like Burgers, Omaha, or Singapore. Moscow is a rather old zoo (1864) which suffered for years under the shackles of communism. It takes some time to overcome such a thing. Russia itself has not thoroughly grasped capitalism the way the Czech Republic, (East) Germany, and Poland have, thus we cannot expect Moscow to be at the level of Prague, Leipzig, or Wroclaw. But as CGSwans points out, there's a lot of construction going on at the Moscow Zoo, thus lots of reasons for optimism.
I personally compare Moscow to the Berlin Zoo, though not quite at that level yet. Moscow's exhibit quality is slightly behind Berlin's, and its animal collection in comparable. Moscow has 1,184 animal species, which is 4th in Europe behind only Berlin, Plzen, and Cologne. It has 166 mammal species, again 4th behind only Plzen and the 2 Berlin zoos. While they don't have any high profile animal superstars (giant pandas, koalas, manatees), they do have a very "complete" zoo, with almost all of the animals one would expect from a complete zoo. One more thing, Moscow is Europe's most attended zoo, with over 3 million annual visitors -- over 5 million if you include all of the children and military veterans who are admitted free.
Yes, they have that big collection, but it's pretty much off-display. The line-up I saw was nothing out of the ordinary for this trip, and easily surpassed by some zoos.
I am certainly hoping Berlin will have a more than 'slightly' better standard of exhibitry, though I don't expect it to match the likes of Zurich or Prague.