I want him to go.
*I want his going.
*I want his going for good.
I want him to go for good.
I want his going to be for good.
*I want him going to be for good.
His going is for good.
?Him going was my idea.
*Him going is for good.
'His going' can be the antecedent of the covert subject of 'to be for good', and can be the subject of 'is for good', but 'him going' can not. That is because 'his going' is a discrete unit, but 'him going' is not. 'Him' is at the right edge of one unit, and 'going' is at the left edge of the following unit.
I don't like him.
I don't like for him to take you out.
I don't like him for taking you out.
I don't like him taking you out. (generalization, or projected incident)
?*I don't like his.
I don't like his taking you out. (generalization)
?*Him taking you out has got to stop.
His taking you out has got to stop.
?Him taking you out is a good idea. (future incident)
His taking you out is a good idea. (generalization or future incident)
Objective case 'him' and possessive case 'his' behave here as they are expected to do elsewhere. The objective case pronoun's primary bond is with the verb or preposition (preceding), while the possessive pronoun's primary bond is with the 'possessed' event (following).
This results in diferences in formal acceptability and in interpretation. The possessive + gerund construction can appear readily in subject position, while this position is much more difficult for objective + gerund. In subject position, there is no verb or preposition preceding the pronoun to assign it objective case (although it may sometimes get it in other ways; this structure is not utterly impossible.). Possessive + gerund has no such need.
The interpretive difference is often hard to pick up, but it is definitely there. The objective case + gerund construction is associated more clearly with an actual episode than its possessive counterpart is, and the latter is more strongly associated with generalizations.
To claim, as most ESL teachers and writers do, that the difference between these constructions is a matter of formality or of literary style, c'est aller un peu vite dans la besogne.