On the flip side of that, business property should be taxed on property's actual value, because it is actively making money using that property, so the business should be able to recover the difference in value through the use of the property. If it can't, then that business isn't making effective use of a scarce resource (commercially zoned real estate) and should make way for a business that will.
That's what bugs me about California's Prop 13. People get stuck in their homes and can't afford to move closer to their jobs because they'd take a huge property tax hit, but businesses just lease from land management companies that own properties forever (literally, because businesses don't ever really die), thus artificially deflating their costs and encouraging businesses to locate themselves in places where housing is most expensive rather than in the suburbs where most of their employees live. All of these factors put serious strain on the highway system, on workers, etc.
And rental housing units have artificially deflated rent because they aren't subject to property tax increases based on the value of the property, thus making it harder and harder for people to justify buying homes. As a result, whenever there's a recession, the housing market falls significantly faster in California than the national average.
If you ask me, property tax should be limited to property that is used commercially, either for a business (not including small businesses run by an individual within his or her home) or for rental purposes, and should be eliminated entirely for personal residences (or at least for your primary residence). This would go a long way towards fixing a lot of problems with one simple law change.