I went for Bristol zoo in this poll. Admittedly I may be biased because I have visited there and have not visited Colchester.
In terms of prosimian primates Bristol has a greater range of species : Slow loris, crowned lemur, aye-aye, ring tailed lemur. Colchester does have the ruffed and red bellied lemur but Bristol also historically held the red ruffed and black and white ruffed lemur so things even out in that regard. Also worth mentioning that tarsier, potto and galagos were also historically kept by Bristol so that is another card in their favour.
In terms of New world primates Bristol currently has five species comprising different families and three of these are endangered and of conservation concern. If we consider previous species held like the black lion tamarin, night monkey and Goeldi's monkey then this only boosts them up in my opinion. Three species held by Colchester all of which are of conservation concern give them a decent hand but point down on Colchester's website from me because they listed on their animal filter the golden headed lion tamarin as being "Asiatic" which is a bit silly.
In terms of Old world primates / monkeys there is admittedly only currently the lion tailed macaque at Bristol which when compared to the L'hoest's monkey, gelada baboon, barbary macaque, patas monkey and mandrill at Colchester (all of which but one is of conservation concern) gives the latter zoo a stronger hand than the former. However, if we consider former holdings of old world species kept at Bristol zoo though the list includes Javan langur, colobus monkey, silvery langur, De Brazza's monkey,
In terms of lesser apes both collections have a single gibbon species, Agile at Bristol and Pileated at Colchester, both of which are endangered so they are pretty even in this regard.
When it comes to great apes Colchester currently keeps more with their orangutang and chimpanzees than Bristol's singles species, the Western lowland gorilla. However, consider for a moment that Bristol in its long history has also historically kept chimpanzees and orangutangs in addition to gorillas and things become more evenly matched.
In terms of conservation output with primates things seem quite even too. Bristol's current campaigns include the Ankarafa field station (which is an important conservation research centre for studying lemurs) and projects in Northern Madagascar involving lemurs (blue eyed black lemur, Sambirano mouse lemur and sportive lemurs), a project with the Sanja mangabey in Tanzania and contributions to the effort to conserve the Western lowland gorilla in Cameroon and Equatorial Guinea.
Colchester by comparison also is involved in in-situ projects in Madagascar with lemurs, with chimpanzee conservation in the Congo, the Gelada baboon project in Ethiopia, Orangutang conservation in Borneo and brown spider monkey in-situ conservation in Ecuador. However, Colchester's support seems mainly along financial lines whereas Bristol's is not only financial but also logistical and in terms of backing long-term studies and assessments which puts them above Colchester IMO.
