Right, I'm back.
In terms of Africa, both associations are relatively strong, with ZSL likely winning given their strong coverage of various habitats on the continent (particularly the Congo in London's case, while Whipsnade has a strong savanna area). Furthermore, there aren't many poor exhibits for African animals that I can think of at ZSL (only really the ungulate exhibits at London). Meanwhile, most of Whitley's exhibits for African animals are in the substandard to average bracket, with only a few such as the Diana monkey exhibit at Paignton surpassing this.
In terms of Islands, I can't exactly remember the boundaries and criteria, so species like Sulawesi crested macaque and babirusa may or may not be up for debate. However, Both zoos have some very nice contributions to make in this category. In terms of Australia, Whitley has a fairly clear-cut advantage, with a much greater variety of species and a much better representation of the continent as a whole. However, the other islands are a different story, with Madagascar in particular being a strong point for ZSL (in particular London). They have some truly fascinating rarities (Aye-Aye, White-tailed antsangy, Narrow-striped mongoose) and some nice exhibits to couple this with. Whitley are possibly stronger from the point of view of South-east Asian islands, with a nice exhibit for Sulawesi macaques in particular and some nice species as well, although ZSL do also have Philippine crocodiles.
In conclusion, I think it is a fairly straightforward 3-2 win for ZSL - I don't think Whitley have enough in the way of quality exhibits for fascinating island species to threaten ZSL's intriguing lineup in that respect.