Humidity does affect air pressure (water has a different mass than air)-this is how a barometer (which measures air pressure) can help predict the severity of storms (H20 weighs less than the N2/O2 mix of air). Altitude affects air pressure because the higher you go, the less air is above you to press down on you. Therefore the answer would be unequal heating.
However, temperature affects density. If there was equal heating, you would expect higher temps to lead to lower pressure, and vice versa. In practice, humidity and altitude are the most important modulators of atmospheric pressure.