I agree that primates are not Antwerps strong suit, and I'm not sure how I'll vote yet, but I'm going to try and make the case for Antwerp here.
First, obviously the Congo Gorilla Forest at Bronx is miles beyond anything Antwerp has, there's really no question here.
However, I do believe that Antwerp does have a chance in this match.
Let's start with the main, and best primate exhibit in Antwerp: Valley of the Great Apes
This primate complex started in 1957 with small outdoor yards, and then an even smaller offshow area. Then in 1989 the moats were filled, significantly enlarging the enclosures, and the entire outdoor yards were covered. This lead to an all-indoor situation that existed until 2018, when the current outdoor aviaries were added. This addition almost doubled the amount of available space for both the chimpanzees and the gorillas.
At this moment, the zoo is home to 5.1 chimpanzees (between 41 and 27 years old, so quite an old group) and a breeding group of 1.4 gorillas. I also expect that the chimps are a phase-out and that Antwerp will move its focus completely to gorillas.
I think that this complex is definitely world-class, and while it can't compete with the Congo Gorilla Forest on looks or size, the gorillas and chimps in Antwerp have a great enclosure that is perfectly suited for their needs. That's pretty admirable, considering that most of the building was constructed in 1957.
The second area is the small monkey house, which is not nearly as good as any of the recent renovations/expansions, but that's mostly because it was constructed in 1978. I'll admit that it looks horrible, but I think that these enclosures are mostly adequate, with plenty of branches and ropes, as well as multiple connected enclosures for the larger monkeys. When I visited today there were 11 species in 12 enclosures. From these 12 enclosures, the only ones that I think are inadequate are the ones for the guereza, and the one for the Hamlyn's monkeys. These two species each have 2 connected enclosures, but the total useable area is quite small.
The monkeys all breed quite well, with a Hamlyn's monkey born in 2017, a guereza in 2018, and a spider monkey only 2 weeks ago.
All in all, I think the small monkey house is adequate, but it needs an update. Not desperately, but it's needed.
Finally there's two more species of primate in Antwerp: the Humboldt's night monkey and the Bolivian squirrel monkeys. The night monkey is almost certainly a phase-out as I haven't seen more than one for a while now, but its enclosure is good if not great, and it is definitely a cool animal to see. The squirrel monkeys have access to one of the two Andean bear enclosures, and this is also a very nice combined species-enclosure.
Something else that is important to mention is the Centre for Research and Conservation (CRC), the research division of the Royal Zoological Society of Antwerp. This organistaion is one of the foremost primatology authorities in Europe. It also set up two primate-related conservation projects, namely Projet Grands Singes and BioBrasil. The former aims to protect great apes in Cameroon. The latter researches genetics in golden-headed lion tamarins and works with local communities to improve awareness of the environment, thus aiding the survival of the tamarins in the wild.
As a conclusion I think it's fair to say that the primate collection at Antwerp is impressive for a zoo its size, and the enclosures range from okay-ish to great, with nothing that's truly awful. There's some work to be done, but over the past decade the zoo has shown that it can capably renovate so that zoonerds and regular visitors alike will enjoy the zoo. Add to that the not-unimportant research the CRC does, and I think it's quite hard to not even give Antwerp 1 point here.
EDIT: Something I forgot to mention are the slow lorises in the Nocturama. Antwerp breeds these quite often (I might be wrong, but I think 2 babies were born this year alone), and their enclosures are good as well.