I'd say they will make too little difference to power consumption to notice. Let's say you are driving at an average speed of 50mph and a consumption of 4 miles/kWh. In one hour you will use 50/4 =15 kWh. Lets say your headlamps use 100W, so in an hour 0.1 kWh, and the LEDs can cut that to 20W, so you save 0.08 kWh. The saving in battery energy would be 0.08/15x100= 0.53%.
The thing about the rain could be an effect caused by diffusion characteristics of the tiny beam from each emitter, which might be a feature of a poorly designed bulb, or, more likely, a mismatch between the optical characteristics of the bulb and the lamp housing. If the latter, maybe that would not be the case if the bulb and lamp housing were matched in design by the original manufacturer.