The OP wanted to know the semantic difference between these two phrases. Once I refocused on this question, I started to formulate some ideas about semantics within larger contexts. Then I stumbled uponThe OP clarified that he/she wanted to know the semantic difference between these two phrases. I will maintain that, for the general reader, both sentences are generally considered acceptable, and the semantics are identical for practically all purposes. There are some subtle variations in style or meaning in which one form might be better than another.
My position is supported by an absolutely outstanding paperwork, with an unassuming name, General properties of Gerunds, Participles and Verbal Nouns (PDF). (Cornilescu, Alexandra) that goes into great detail Based on many facets of this complex issue, including this exact issue of semantics. The above mentioned article seems to be part of a larger work, Complementation in English: A Minimalist Approach
It appears that the best research so far on the theoretical answer to this question is directly or indirectly referenced in there. I haven't the time to dig into this and refactor my answer at this point. Just search the General properties of Gerunds, Participles and Verbal Nouns for semantics
to find relevant information.
For reference, general searches to find these works, see:
Based on the article,phrase "his telling me" seems to be more traditionally (perhaps prescriptively) correct. Also, "him telling me" has more of a feel of an independent clause (aka IP), "subject verb object", while "his telling me" is more like a dependent clause (aka DP). The author also indicates there is ambiguity in how to parse these. Don't hesitate to search the General properties of Gerunds, Participles and Verbal Nouns for semantics
to find additional relevant information.
I will maintain, however, for the general reader, both sentences are generally considered acceptableI want to highlight this work (and the author) and encourage an interested linguistics reader to investigate further. It's a very interesting (advanced yet sometimes very readable) exposition on many facets of this complex issue, and theincluding this exact issue of semantics are identical for practically all purposes. There are some subtle variations in style The above chapter seems to contain (directly or meaning in which one form might be better than anotherindirectly via reference) the best research on the theory to this question through the publication date.
FinallyFor reference, the above text is part of a book (also with an unassuming name), Complementation in English: A Minimalist Approach (Cornilescu 2003, Google Ref) I must say Alexandra Cornilescu has many outstanding and intriguing papers/books that I'll be reading. Here's the Wikipedia Page (translated) about him.
General searches to find these works, see:
I haven't the time to dig further into this at this point. Anyone else is free to use the source I've provided to create/enhance their own answer.