If you like pygmy hippos you needn't worry as both collections have them! As a long-time member/visitor to both collections I will boil down the best things about each:
LONDON = Walkthrough exhibits abound, from lemurs to squirrel monkeys to a rainforest exhibit to butterflies to birds to spiders! Not to mention a very good reptile and aquatics collection. Large mammals are on the low side in regards to quantity, and a few carnivores (hunting dogs, lions and tigers). They have gorillas and one of only five breeding pairs of aye-ayes in Europe. The enclosures can seem/can be small, but that's what comes with a city zoo I'm afraid. Lots of shelter and indoor areas, but can get very busy and quite expensive due to its location.
WHIPSNADE - A LOT of walking, but much more space due to its location. All the larger animals are here; elephants, rhinos, common hippos, bears and sealions. Much better butterfly and lemur walkthroughs than London, but those are the only decent ones in all honesty. The train is worth it as it allows you to see Passage Through Asia (a large Asian exhibit with deer, yaks, wild horses and camels) unless you plan on driving around Whipsnade in which case you can drive through PTA yourself. Chimpanzees here, not the best enclosure for them but it does the job. The penguin pool is much smaller than the one at London. Larger number of carnivores (lions, tigers, cheetahs, bears, wolverines, lynx, sealions) and the giraffe herd is much bigger with the added bonus of babies. Red pandas too. However shelter wise you won't have much going for you so only go if the forecast is going to be good. Due to the size it can also be a lot quieter than London, plus there are astounding views of the surrounding countryside from the top part of the zoo.
