For him not going to party was a big mistake.
His not going to party was a big mistake.
I think in the first sentence gives a sense that he is sad as he missed the party. The second sentence gives a sense that someone was in the party and enjoyed, now he is trying to say how wrong his decision was.
Maybe, I'm thinking too much on these sentences. There is no context, just these two sentence. Would you please explain the actual meaning and the grammar behind these sentences, if I'm not thinking right.