I am not just my memory. My identity and being is closely entangled with my life, my environment, the people I interact with, the physical effects on me and my body. Everything that has an effect on my future self basically (weighted by causal distance or something).

And the scenarios differ in that: The branch Omega tortures has practically no causal effect on my future self after the week (except my absence for a week, which is a comparatively small effect given that many people leave their home for muh longer times without much effect).

The millionaire on the other hand may plausibly have a much more stronger effect. At least that is how I model it. Part of it surely is that the Omega example is constructed to have no other effects - thus I assume all other lfe-entangement-effects to be small. Whereas for the millionaire example all my caveats regarding humans proposing deals apply.