So we don't really know how big of a deterrent anything is, including nuclear weapons. We assume there was some deterrent action there, but deterrence is a psychological effect and is not easy to measure. It's very hard to determine, historically, "if factor X had not been there, then Y event would have been the result." This has led to some people claiming deterrence is a myth, though I think that probably goes a bit far (it seems unreasonable to me to assume that these arsenals did not factor into the broad context of what seemed like a good or bad idea). But it is true that it is hard to pin down exactly how much of a deterrent effect they had, much less versus other effects (e.g., economic effects, political effects, diplomatic effects — there are often lots of reasons not to go to war).

Anyway, given that we don't even know how much deterrent effect to ascribe to nukes, it's unlikely we're going to get a good sense about chemical and biological weapons. But on the whole, nuclear weapons were deployed in far greater numbers, and with far more sophisticated delivery vehicles (ICBMs, SLBMs, etc.). The other WMDs were considered minor by comparison. And while chemical and bio weapons loom as particularly nasty in public perception, experts tend to think of them as pretty small in their effects compared to nukes. They're bad, but they're not nuke-level bad.

One can ask: if nukes weren't around, would the others have had a similar effect as nukes? But again, that's totally hypothetical — we don't really know, and it's not clear how you'd measure such a thing.