First question has to be - do you favour primates or ungulates?
West Mids has only a single primate species (bizarrely, the Aye-Aye) but a very good ungulate collection including Sambar, Barasingha, Philippine Spotted Deer, Addax, Brindled Gnu, Nilgai, Cape Buffalo and Banteng, as well as a large group of hippos. It also has a better reptile collection than Twycross - King Cobra is a particular highlight - and more large carnivores - generic and 'white' krugeri lions, normal and white 'Bengal' Tigers, Cheetah, Amur Leopards, wolves and African Wild Dogs.
Twycross has an excellent primate collection (including Phayre's Langur, Red-bellied, Crowned, Lowe's and Lesser Spot-nosed Guenons, among others, Woolly Monkeys, 3 species of spider monkey and four species of great ape, including the UK's only Bonobos and some very odd 'chocolate' chimps. There are some interesting small carnivores, including Aardwolf, Dhole and Bat-eared Fox, and a breeding group of Michie's Tufted Deer.
Both have lions, giraffes, elephants, crocodiles (though they're quite a bit bigger at WM), camels and Amur Leopards. ALthough neither are really bird collections, Twycross does have some little gems tucked away, including Purple Heron and Little Pied Cormorant.
On balance, if you've done neither before, there's probably more new stuff (and more species overall) to see at Twycross.