There really is not much difference in these two constructions. One could make a case that the speaker is more annoyed at the situation in the first case and the person in the second case, but I'm not sure about that.Originally Posted by navi
At one time, the second construction was considered a grammatical error. The first construction uses a gerund as the object of the verb "resented" and it is modified (because it is a noun) by a possessive adjective. Along the way, language users started using the objective pronoun instead of the possessive pronoun (probably as a mistake), but this usage caught on. These days, both constructions are accepted, but some still prefer the possessive version.