The most distinctive twists I've encountered involve the existential dread of the reincarnated character's situation, something many stories gloss over. Imagine waking up as a toddler Jon Snow with a modern mind—you'd know about the White Walkers, the Red Wedding, everything—but you're physically and socially powerless for years. That creates a psychological tension I haven't seen much elsewhere in fanfiction. Some writers lean into this, making Jon's 'knowledge' feel more like a curse, causing paranoia or driving him to make different, potentially worse, mistakes.
I also appreciate when the twist isn't just about Jon gaining power, but about his relationship to the Stark family being fundamentally altered by his outsider's perspective. He might be colder to Catelyn, knowing her future resentment, or he might try to 'fix' things for Robb and Ned in ways that backfire spectacularly. I read one where his attempts to prepare for the Long Night made him seem mad, and he was eventually sent to the Citadel, which completely derailed the canonical path in a believable way.