Temples for order - law vs. happiness

Ok, you can build two different temples, one with 10% public order for happiness, one with 10% public order, 5% law, 5% happiness. What's the difference if they both produce order. Does the one for law reduce corruption maybe? Then what's the advantage of additional happiness? Any ideas? Thanks.

Grifman

Yes, buildings that are relevant to Law or Academics cut down on corruption and I believe improve overall efficiency regarding tax collecting. Happiness simply makes your city's inhabitants less likely to revolt and increases the birth rate.