In our everyday life, does the temperature or humidity have a greater effect on how fast things dry? Are there any theories/models that explain this quantitatively?
It is just a mass transfer that is driven by the difference in vapor pressure of the liquid versus vapor pressure in the vapor phase.
If the relative humidity is 100% then you are not going to get any evaporation. Even at 100 °F.
But if the humidity is 0 you will get pretty good evaporation at 40 °F.
All that really matters is relative humidity. But as you increase temperature for the same absolute humidity the relative humidity goes down.