I've visited 3 in the last 2 years and whilst all Banham & Africa Alive have their merits and relative rarities, my personal favourite would be Thrigby Hall, as that has more species I don't regularly see elsewhere.
Having said that, it is also the smallest of the three and not a full day. It's considerably cheaper than the other two as well.
AA is not technically in Norfolk, indeed it used to be called Suffolk Wildlife Park. That said, it's a nicely done place, virtually all the exhibits are pretty well done and it has a few nice oddities -Aardvark (best seen first thing) Fossa, Striped Hyena, Somali Wild Ass, Barbary Sheep, Straw-colored Fruit Bat, Blesbok and African Barn Owl.
Banham Zoo is is a similar set-up (reasonable enclosures, some oddities), but quite a bit bigger, with good animal shows (armadillo, amongst others) and Bird of Prey Display (multiples vultures flying in low, just above your head).
Amazona and Thrigby are smaller, have are a little more "homespun" feel, and don't change much year to year. They both have a handful of extreme rare species (in terms of little or no other UK zoos holding them)
but a lot of them can be inactive, and barely, if at all, visible -if you go to either prepar to be patient if you really want to see a specific species. Finally, the cafe veranda at Amazona is, in my opinion, one of the nicest places in a UK to sit and have a drink and snack/cake.
Shorelands sounds a nice place if you like birds and the owner has a great track record but I've not visited yet and am unsure if it's properly open.
Finally, if you've got a time machine I'd check out Kilverston (and take me with you

).