It somewhat depends on the zoo and what you're going to take photos of. Some zoos are very up close, others have quite deep enclosures where a longer lens helps.
It can also depend what style of photo you want, a long lens even closer up can let you take portraits whilst a wider lens might give you more of a whole body shot or several interacting.
Personally I'd likely take both and put the 70-200mm on the camera first and see how it goes. It's a very good and flexible focal range to work with and you can then always spend a few moments swapping over to the 400 for some enclosures.
Note remember to be patient. Many people rush around the zoo and think they are done in an hour or two. If you spend time at each enclosure you've often far more chance of getting better shots. Though keep an eye on things like keeper talks and feeding events because many animals will often be quite lazy (eg big cats) but when feeding time comes htey can get far more active.