I have visited both zoos a few times in the last 15 years.
PRO for Hamburg:
- the already mentioned historic exhibits and atmosphere as well as the more interesting other stuff the city has to offer (harbour sight seeing tour, Reeperbahn, Hamburger SV a.s.o.)
- the gardening character of the Tierpark
- the option to visit the new Troparium (adjacted, but extra entrance fee) with reptiles, amphibians, fishes and invertebrates (there are only a few in Hannover)
- giant river otter
PRO for Hannover
- more or less new zoo (most exhibits are not older than 15 years)
- boat tour (included in entrance fee) thru the african part (very good)
- immersion exhibits (north african houses with north african animals, asian jungle palace and the complete new "Yukon Bay" with in Europe seldom shown Karibous
- the better zoo food (asian food in the middle of the jungle palace, good german food in the Meyers Hof area)
- a good childrens play area
- Kaama-Hartebeest, Common Wombat
Short: If you are travelling with kids, go to Hannover, otherwise go to Hamburg.