Ok here is what I know:
When there is humidity in jet engines then the air density decreases hence less air to move and burn at the combustion chamber which will degrade the performance.
However the amount of degradation is not very noticable in that most combustion chambers are designed to work with average humidities expected in humid areas (they are tested and thier design is made such that they can withstand certain amount of water droplets), Also on modern engines since most of them are turbofan and most of the thrust is produced at the bypass (around 70% of the air intake goes through the bypass) and not the exhaust the effect is even less since the combustion chamber takes less air.
However heavy rain or water ingestion can cause an engine flamout if its on idle power.
Piston engines rely 100% at the combustion chamber output (unlike turbofan engines which rely on the air discharge at the bypass) to produce the pistons mechanical movements and if the fuel air mixture gets disrupted with water which is a foreign matter the combustion chamber perofomance gets degraded hence the effect of engine performance is more since the combustion chamber reliance is more.