Ok so I'm hoping to visit the city of Berlin on the week of the 22nd of April for my Spring break and am quite eager to see both zoos. Just got some quick questions
What's the weather usually like?
Do either of the zoos require more than 1 full day?
How easy is it to navigate for an English speaker?
If you stay about a week in late April, you should hopefully have at least a day or two with fairly nice weather (usually, May is the nicest month of the year if you don't like it too cold or hot).
My advise would be to pick the Tierpark for one of those really nice days. Other than that, I would focus on the main attractions in the Tierpark like Himalaya, Savannah + vultures, penguins and cheetahs as well as Brehm building, monkey building and lemur forest. These are easy to find and you'll discover some nice enclosures and great species there. Also, the new Asia exhibit will be open by then (it's on the main way coming from the old castle, passing the main restaurant and going up to monkey building and Himalaya region).
If you do plan to see all exhibits, I would recommend using one of the old maps still available online (just search for "Tierpark Berlin map"). Many species named/depicted of course won't be correct (and you can forget about the lower left corner) but this way you won't miss much.
As for the zoo you shouldn't have much of a problem to find your way and the exhibits and even mediocre weather shouldn't be (as) much of a problem.
Now a highly subjective matter:
For both zoos I would say you can either fully enjoy your visit or really try and see everything on just one day (including returning to not-showing animals). To me, the greater beauty lies in immersing in the beautiful park landscapes, staying open and curious as to what the animals are going to do etc. If I miss some exhibits this way, I don't really care. Of course, in this case I could revisit these particular zoos any month (in theory). But I go about it the same way wherever I go.
When I went to Zoo Munich, I think I did all important bits in a day and I loved it (and I never really checked, if I missed a bit). The same applies to other visits as well.
However, in Cologne we did try to see most parts, were a bit unlucky with the official highlights like Hippodom and elephant park (former: glass and water were bad, latter: no active life, no green), also didn't enjoy the rest of the zoo very much and still didn't have time for the aquarium part
(in both cases I wasn't alone, though but I think it wouldn't have been much different on my own).
So I think you could have the same experience in Berlin, try and see everything in a very short but miss the beauty and magic of these places (if you have a similar attitude like mine). This potential is far bigger for the Tierpark, though. So if you want to see it all and possibly get to divide 3 days for it, I would rather take 2 complete days for the Tierpark (even though it may seem unfair for the Aquarium, bird house, carnivore building with night/nocturnal section, sea shore aviary etc in the zoo)...