It's stated and heavily implied throughout ATLA it amps them by a relatively big degree. Whether or not it 'seems to not do anything noticeable' is irrelevant. The Fire Nation halted their attack on the Northern Water Tribe when it was nearing night time for the sole reason that the moon amped them to such a degree that continuing the attack would be dangerous and quite costly.
Of course it's speculation how much it would amp her, but none of what was stated about the full moon is hyperbole. It's a hyperbole because we don't know how powerful it makes her? That makes 0 sense at all. All we know is that it amps waterbenders, and it's been stated outright by Katara that she noticed her waterbending is stronger at night. That should be good enough for you. I don't know how much it amps waterbenders, and that isn't even what we're discussing, we're discussing whether or not the amp would be significant, which it pretty obviously is considering the Fire Nation halted their invasion because of the amp it gives waterbenders.
Don't ask me how much her power level increases, I don't know that, but what we do know is that in general a waterbender's power is increased.
Originally posted by yungz22
Id even wager that gaazan can beat katara even with a full moon. The power isnt that significant compared to sozens comet. Zuko still beat her during the water tribe invasion
Only after the moon went away. She kicked his ass with the moon and he specifically noted the difference it made not having it.
Almost every king/ tribe leader except for the earth king was seen as very powerful benders except for the earth king. And it seems that the earth kings and queens of ba sing se arent too popular with the public anyway.
Regardless my point still stands katara is not as legendary or as respected as zuko around the world.