Differences between gene expression expressed as z-score or log2 values in Allen Brain Atlas

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Hi everyone,

This is a question from a complete beginner on this matter.

In the Allen Brain Atlas website, why is that log2 values are sometimes very different even for similar z-score values? For example:

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I noticed that log2 values are quite stable within a given probe, while z-score values are more stable between probes. Is this because they are normalized by different factors?

Which score would be better to use if I want to compare expression differences between genes?

Thank you.