I have no way of knowing which is the more natural choice for native speakers but I would avoid No. 2. There is no grammatical justification for the object form him.
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GuttyonCould you tell me which is more natural between 1. and 2.?They are equally natural. (The accusative form him is a bit informal.)
1.His doing it…
2.Him doing it…
Cool BreezeThere is no grammatical justification for the object form him.If you’re going to use that reasoning then you might also say there’
Aspara GusIf you’re going to use that reasoning then you might also say there’s no justification for it in It’s him, either. Nevertheless, it is standard English.I know that. Even me is standard English in replies like this:
ozzourtiWhile you can justify the use of the subject case in It is I, I don't think you can justify its use when the pronoun stands alone.It seems to be that way in English!