All in all, while I do think Chester beats Bronx in terms of invertebrates and fishes (Chester keeps/breeds a larger variety of endangered South Asian Cyprinidae afaik), Bronx clearly dominates when it comes to herps. While Chester certainly has some major accomplishments under their belt (namely the repeatedly tuatara breeding), in general the zoo seems to have an increasing lack of interest in herps and I've noticed they've been reducing the overall collection size quite substantially since my initial 2016 visit, whereas Bronx has been steadily increasing their collection as well as taking on more complicated and endangered species in the past few years. This, combined with their unmatched conservation programs, lead to a clear 2-1 victory as far as I'm concerned.
When looking at the latest stock list, Chester did actually increase the number of reptile species they keep (58 at the start of 2019 against 53 mentioned in the IZY), whereas number of amphibians remained stable at 29.
Btw. are there any proper pictures showing the inside of the Reptile house?