I think the key point is that, gasoline engine is under stoichiometric combustion, while diesel engine under lean fuel combustion. The difference in combustion makes the water content in the exhausts of two kinds engines different, it is higher in gasoline exhaust, thus, the water in gasoline exhaust condenses easier than that in diesel exhaust. That's the dripping water you have seen.

I am not sure about the difference. probably i will check the following points:

1. check for Jacket water leakage in the valve seats/cylinder etc..If the  jacket cooling water is connected to expansion tank i.e for closed jacket cooling water system. we can estimate the leakage by confirming any turbulence in the expansion tank or by measurement of cooling water consumption with heat loss( for normal and abnormal condition).

2. Check  the oxygen concentration , lambda value at exhaust by exhaust analyzer, when comparing both the fuels. which will give some  direction to understand the combustion  chemistry of  the condition. water  at exhaust can be of cooling water leakage or excess oxygen/air  for combustion.

3. i hope both comparison is for natural aspirated engines with  the same mass flow rate of air . check for the load conditions, mass flow rate of air for comparing both the engines.

Water is the combustion product of the in cylinder in both the engines but due to difference in the combustion type , diesel generates more of soot and less of water.Again for same distance traveled diesel engine uses less fuel than gasoline hence on combustion will generate less water than gasoline.

I hope the question is referring for the same relative humidity in the inlet. As Abhijeet stated, water is a product of combustion in all internal combustion engines. Usually we expect similar content of water vapor in the exhaust of both engines. I would rather relate the difference in the two engines due to the different in exhaust temperature.

As previously stated, water (vapor) is one of the two main products of combustion in all engines. Humidity of inlet air has for sure an impact on the outlet water content, but the formation of liquid water is mainly dependent on exhaust temperature at the exhaust pipe exit. That parameter is influenced by exhaust temperature (typically higher in gasoline engines), pipes lengths, after-treatment devices operative conditions, transient conditions and so on... For that reason, if the operating condition is comparable, I think you can't state that in general gasoline engines drip more water than diesel one.

water drips from vapor depends on dew point temperature, saturation pressure, specific humidity and relative humidity. As compression ratios are very much high in case of diesel engine, pressures developed during combustion and at the compression stroke are vergy high. Hydrogen evoved during combustion will be converted into soot partciles along with carbon or particulate matter. Hence chances of morewater vapor formation are less for diesel engine rather than gasoline engine. 

I think the key point is that, gasoline engine is under stoichiometric combustion, while diesel engine under lean fuel combustion. The difference in combustion makes the water content in the exhausts of two kinds engines different, it is higher in gasoline exhaust, thus, the water in gasoline exhaust condenses easier than that in diesel exhaust. That's the dripping water you have seen.

I agree with Maddali and Ftwi Yohaness. Formation of liquid water and the exhaust tailgate is the combination of exhaust temperature and ambient conditions. If the parameters meet the dew point conditions, then liquid water is formed. However, since soot is present in the diesel combustion products, it could be possible that some water vapor will absorb the soot particles, thus resulting in less liquid presence at the tailgate (just a thought).