Both possibilities are likely, yet we disagree about the one which is most likely.
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After years upon years of mentle struggle, the new wielder would become a broken slave to the ring
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A small mind would become enslaved to the Ring and therefore be overpowered by it. But it never says it would do the same to a great mind, I believe (but here I might be wrong). There's quotes that I know about the corruption of heart and mind and therefore becoming the new Dark Lord, but I don't think a mind great enough to control the Ring in the first place would become enslaved to it, except in wielding it for his own desire.
Therefore the wielder would not be yielding to the Ring's will for Sauron, and Sauron would never become great enough to overpower the wielder of the Ring.