It's been three years since this discussion started, has anything changed? Which 3 or 4 zoos in Europe would you now recommend?
Those who live in Europe are best qualified to answer. However I have made five trips there (most recent last month) and have visited zoos each time, though not as many last two trips as my interest in zoos is waning. I will list the ones I have personally visited in order of preference, as in the first on the list is my favorite, then second favorite and so on. Please note my preferences are based on wild cats, large mammals, large enclosures and photo opportunities. Some that I list near the bottom would be listed near the top by others due to their history or variety. Le Parc Des Felins (France) Heritage Wildlife Foundation (England) Highland Wildlife Park (Scotland) Chester Zoo (England) Rare Species Conservation Centre (England - now closed) Port Lympne Wild Animal Park (England) Langenberg Wildlife Park (Switzerland) Zoo Salzburg (Austria) Zoo Zurich (Switzerland) Edinburgh Zoo (Scotland) Zoo Vienna/Schonbrunn (Austria) Parq Zoologique Du Paris (France) London Zoo (England) Howletts Wild Animal Park (England) ZooBotanico Jerez (Spain) Le Menagerie (France) As I said my preferences are very specific and other considerations (history, etc) would change the order. I am sure there are people reading this who are yelling at their screen and wondering what kind of idiot would place Heritage Wildlife Foundation above London Zoo or Schonbrunn.
As ArizonaDocent well knows, his list is almost useless, unless you are a felinophile I recommend this thread: https://www.zoochat.com/community/threads/top-10-and-top-25-european-zoos.343268/
And willing to take into account his tendency to skip any parts of a collection which don't either contain a cat species, or lead him towards an area which contains a cat species
Thank you all for the wonderful replies. In regard to species diversity, would you recommend Rotterdam/Amsterdam & Berlin/Leipzig? I want to see as many species as I can.
For species diversity, I would suggest Prague/Pilsen and Berlin/Leipzig are probably the top priorities - honourable mention for Wroclaw/Poznan as well. Not been to Artis for some time but instinctively I think your best Dutch bet would be Rotterdam/Arnhem (and I'd add Apenheul as well!).
I tend to agree with "Maguari" here; Prague / Pilsen and Berlin / Leipzig are definitely the two combinations I would recommend for zoos with a high species diversity. However, in addition:- If you're especially interested in birds then a trip to Walsrode is essential. And if you're interested in cetaceans you should also consider visiting Duisburg whilst the South American river dolphin is still there; it has been at Duisburg for forty-two years and, when it eventually dies, I doubt we'll ever see another one in Europe.
As Tim May wrote, Duisburg would be a good choice, connected with a visit at Cologne Zoo and Zoo Wuppertal (both have a big collection/high species diversity and are close to eachother and to Duisburg).