There are a number of problems with bioweapons, as opposed to blast weapons (of which nukes are just bigger and better). Bioweapons take time to work, they are difficult to use/get them to where they need to be. There is always the risk of them spreading to affect your troops or civilian population. Realistically speaking it would be the mid-1950s before you could get bacterial agents that were useful - with bacteria you would want to make them resistant to usual antibiotics, of course that means you need to have something that works. Immunizations vary in effectiveness depending on disease, and even if effective need to be repeated in most cases.
Nowadays gene manipulation allows you to have a shot are manipulating bacteria, rickettsia, and viruses for weaponization. The risks remain, and as HIV (and the common cold) show, producing effective vaccines or treatments can be quite challenging. Making "superbugs" of any of the infectious agents listed is very risky as if they are difficult for you enemy to control, expect the same for you if they get loose.
Vegetarian was a strategic weapon that was designed to "poison" farmland, the number of actual anthrax cases in humans you would have seen was pretty low. Unit 731 basically worked on finding the most effective EXISTING strains of diseases, and ways to disperse them. Their efforts were successful against the civilian population where used in China with crowding, poor sanitation etc. It is not clear they had much direct effect on any military units, though of course an epidemic is disruptive.
If you are using bioweapons against a civilian population (which is fixed and not mobile like a military unit), especially at some distance from your own territory, these things can be a strategic weapon. Against military targets they are less effective. Measures against epidemic disease such as surveillance, quarantine, etc are easier to do in a military unit than in a civilian population.