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Have you seen him today?/ Did you see him today?

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There is no real difference.

Clive

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Eileen ChinHave you seen him today?

This suggests an accidental encounter. Your paths frequently cross, but sometimes you see him and sometimes you don't.

Eileen ChinDid you see him today?

This suggests that there was a meeting planned, or that it is customary for him to be in the same place as you are. Did that meeting take place? Was he in his normal place where you see him daily?

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Comments  

Either is fine, although I think the second is a bit more idiomatic.

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