I don't think it's just a matter of closeness of approximation.

• I would feel much better about being replaced by an approximation with an extra 20 IQ points, than by an approximation with 20 fewer.
• I would feel much better about being replaced by an approximation with extra memories of things that never actually happened to me, than by an approximation with lots of memories missing.
• I would feel much better about being replaced by an approximation that had gained a keen interest in (say) cricket, than by an approximation that had lost its interest in (say) classical music.

The common theme here is that gains are better than losses, which is a bit content-free given that that's how we choose what to call a gain and what to call a loss. (But not wholly content-free. Think of it like this: I would be happier about becoming a part of someone "bigger" than I would be about having only a part of me survive.)

• If some version of me is still alive in 50 years and is substantially different in personality, opinions, skills, etc., I think I would feel rather better about it if those changes happened gradually than if they happened suddenly; and better if they happened organically in response to external events, new evidence, etc, than if because someone rewrote my personality.

I fear this is mostly because "normal" things feel less threatening than "weird" things, and gradual mostly-endogenous changes are more normal than sudden exogenous ones.

As for "partial immortality" ... I think James_Miller has a point, which I will make more explicitly as follows: if you are going to grant anyone immortality, then good for them (unless their existence is horrible), so I would be glad about it even if they bore no relation to me at all. Perhaps the actual question is more "how much like me would this immortal being have to be in order for it to feel as if I am benefiting?". I'm not sure that's a question I should be trying to answer -- it seems to be encouraging a wrong way of thinking about personal identity.