Sam: To be honest, I am not an expert on the comparative tax rates of the two communities. I will say this as a general rule:
Tax rates are based on the value of the property. A small single-family house will pay less than a larger one. There is also the difference in neighborhood. Older homes in a so-so area may have less value than a newer home in an upcoming area of the town. The assessment will differ and therefore so will the annual tax.
As far as taxes going down, I guess you haven't been around that long. I've rarely ever seen taxes go down, except after a reassessment (Occurs about every ten years) where the town finds that some homes are worth comparatively different amounts in comparison to one another. The same tax budget gets spread a little differently and some go down while others go up. Same total tax bill.
Different communities have different tax bases. Most town leaders are always searching for high "ratables," bringing in high paying malls, offices etc., rather than housing. So, if the town does not have lots of high ratables, the burden on the homeowner is greater. East Brunswick would seem to have a good mix but that would take a study I'm not prepared to start.