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#NOTE ADDED TO ANSWER

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 upon an absolutely outstanding paper, with an unassuming name, General properties of Gerunds, Participles and Verbal Nouns (PDF). (Cornilescu, Alexandra) that goes into great detail 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:

• Google Search: Complementation in English a Minimalist Approach
• Google Search: General properties of Gerunds, Participles and Verbal Nouns

Based on the article, "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.

I will maintain, however, 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.

Finally, I must say this author has many outstanding and intriguing papers/books that I'll be reading. Here's the Wikipedia Page (translated) about him.

**Anyone else is free to use the source I've provided to create/enhance their own answer.

The following is my entire answer before the above note was created, and I still stand by it's value.

#Preface For the grammar involved, this question has a very good answer in http://english.stackexchange.com/a/2628/61171 (Credit @CopperKettle for reference.) I'll attempt to convey my native AmEng intuition with examples so we can avoid some of the heavier grammar lingo.

Second, let's simplify by giving him a name, "John". Now we can talk about John directly. This is simply a teaching aid.

##Semantics

In isolation, there's no significant semantic difference between the two sentences. They are saying exactly the same thing in slightly different ways.

But in some contexts, the differences could have some differing semantic pull. The issue of semantic differences might be rephrased: If you polled 100 people, what meanings would be interpreted, and what would be the percentage of each meaning?

##Grammar Basics

Let's review some basic grammar.

• he and him are pronouns that can be replaced with "John".

• I saw John.

• I saw him.

• John saw me.

• He saw me.

• his is a possessive pronoun and can be replaced with John's:

• John's bike is green.

• His bike is green.

• I saw John's bike.

• I saw his bike.

Now consider some gerunds in which their function is more clear than the OP's sentences:

• I saw John dancing.
• I saw him dancing. (I saw him doing something. This conveys a sense of action.)
• John's dancing is beautiful.
• His dancing is beautiful. ("His dancing" is the subject. I'm talking about his act of dancing, as if it were a static thing.)

Note in the last example, "His dancing" is the subject of the sentence and functions like a noun.

##FIRST SENTENCE

For the first sentence, his is a possessive pronoun, and "his telling me" functions as a noun. The following sentences all have a similar feel to them (relative to the "him" sentence):

• I know it without his telling me.
• I know it without John's act of telling me.
• I know it without John's advice.
• I know it without advice.

Here's a tree showing a traditional grammar layout of the sentence:¹

Here's a more modern syntax tree:²

##SECOND SENTENCE

In the second sentence, the word "him" is the same as "John". Note the following:

• John told Paul a secret.
• He told him a secret.

Now consider the following:

• It's funny to see John dancing.

"John dancing" has an active meaning. John is hypothetically doing something. Here's a modern syntax tree:³

##Footnotes on Syntax Trees

This section demonstrates how to easily create the images contained within this answer. As such, this section is only ancillary technical information and is separate from the answer proper.

Below, I show how to generate Labeled Bracket Notation and how to render that notation into an image of a tree.

For the modern grammar syntax trees, I went to the the Stanford Parser and entered the first sentence. I substituted [ for ( and ] for ) and plugged that into http://yohasebe.com/rsyntaxtree. That gave a pretty picture. I usually resize these in something like pixlr to make them smaller. These trees use artificial intelligence natural language processing (NLP), and as such, may give less-than-ideal or incorrect results.

##1. Sentence 1 - Traditional Grammar The first sentence I changed to typify a traditional grammar.

[S_Traditional-Grammar
    [Subject I]
    [Predicate 
        [Verb-"know"
            [Object it]
            [PP 
                [PRP without]
                [NP
                    [N-POS his] 
                    [NP
                        [GER-PH^ telling me]
                    ]
                ]
            ]   
        ]
    ]
]

##2. Sentence 1 - Modern Syntax Tree

The Stanford Parser results for the modern syntax tree didn't express what I wanted, so I modified it slightly.

  [S
    [NP [PRP I]]
    [VP [VBP know]
      [NP [PRP it]]
      [PP [IN without]
          [NP his telling me]
      ]
    ]
  ]

##3. Sentence 2 - Modern Syntax Tree

For the second sentence, I liked the Stanford Parser result. It's still slightly simplified.

[ROOT
  [S
    [NP [PRP I]]
    [VP [VBP know]
      [NP [PRP it]]
      [PP [IN without]
        [S
          [NP [PRP him]]
          [VP [VBG telling]
            [NP [PRP me]]]]]]
    ]]