Well, what do you like seeing, and what haven't you seen that you most want to? Whipsnade has Asian Elephants, White and Indian Rhino, Common and Pigmy Hippo, Giraffe, Grevy's Zebra, four species of wild cattle, and a lot of deer and antelope. London has few ungulates but does have Malay Tapir, Vicuna and Okapi. It also has the only Bearded Pigs in the UK.
Both sites have Lions and Tigers, but only Whipsnade has bears (Brown and Sloth), plus Wolverines, Cheetah and Lynx. London has Hunting Dogs.
London has far more primates (but the ZSL Chimps are at Whipsnade). Neither site's bird collection is that special IMHO, but London does have a fine reptile collection (the male Komodo dragon is a magnificent beast), a big aquarium that has fine keepers and an outdated building, and an invertebrate collection that is world-class.
London can be reached without too much difficulty by public transport. Whipsnade without a car is an arduous experience. The latter is also VERY big, and bleak in the extreme in unpleasant weather.
Any serious UK zoo enthusiast ought to visit both, although during the winter months London would be a more comfortable experience.