I just found a quote from the fellowship that I think is pertinent. The quote is Gandalf speaking about Gollum and the discovery of the ring to Frodo in Shadow of the Past.
Quote:
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He was very pleased with his discovery and he concealed it; and he used it to find out secrets, and he put his knowledge to crooked and malicious uses. He became sharp-eyed and keen-eared for all that was hurtful. The ring had given him power according to his stature.
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emphasis is mine.
So Gollum was able to get power for what he wanted to do but it was according to his stature. So it seems that the ring can give the wearer power to match their ability, stature, or will. Now it gives them this power but if their power is not on par with that of its creator, Sauron, then the ring overtakes them. So let's say that Galadriel were to posses the ring, her power would be much greater because of her greater innate strength than would be the power of Gollum. Also I believe that the ring would take longer to posses her than Gollum. First and most obvious because of her good desire as opposed to Gollum's evil but secondly because of her greater innate strength.