To be frank, nowhere can match Chester. But that doesn't mean that the other zoos aren't worth visiting. If you're interested in waterfowl and bird watching, try to get to Martin Mere in the next few months: there is a pretty comprehensive collection of captive waterfowl, but in the winter there are also huge flocks of pink-footed geese moving around the area and many visit or overfly the reserve, add a big herd of wild whooper swans and plenty of ducks, with a good chance of seeing kingfishers, peregrines and a stoat or two.
If you like otters, try the Chestnut Centre in Derbyshire, which also has owls and native mammals in its collection. Knowsley Safari Park or Yorkshire Wildlife Park have larger species, but I haven't visited them myself, so I can't say more - perhaps others can add further information. For primates, you should go to Twycross, although it's a bit cross country from Cheshire. Dudley is easier to reach by motorway and it has some nice exhibits, and plans to improve some of its older ones.