I’ve spent part of this weekend creating slides for a workshop I’m giving on Deep Point of view at the annual In Your Write Mind Workshop (which is sponsored and run by the Alumni of the Writing Popular Fiction graduate program at Seton Hill).
I have seen folks mention that they don’t like deep limited third because they feel that if you’re getting that close to a character, why not write in first? That first person places the reader just as close to the character as deep limited third. That is, there’s no functional difference between first person and deep limited third person.
They are different. I know they’re different. Having written both, there is a certain feel to close limited third that is different than first… and it’s not just because of the pronouns. There’s still distance in first person, though it’s pretty much always the same distance. But I couldn’t articulate why…
And yes, you can have distance in limited third. One of the great aspects of third person is that you can vary the distance between the reader and the character dropping in deep or rising up to give some distance. But there’s less distance between the reader and the character in deep third person than in first person. But again, I couldn’t articulate why.
Then, while combing through my craft books, I ran across this quote from The Power of Point of View by Alicia Rasley about Deep limited third:
This is the most intense and intimate POV level, more intimate, in fact, then first-person narration. Why? Because an effective first-person narrator can and probably will lie. In deep-immersion third person, the reader can assume that what’s reported is the deepest of personal truth, at least as far as the character knows.
And there it is–what I couldn’t articulate. The difference is that a first person narrator can lie to the reader, that is, they can be unreliable.
If there is falsehood in a deep third person POV, it’s not because the character is deliberately misleading the reader, but because the character has deluded him or herself. What you see in deep third is the personal truth of the character. The inner truth. Not the “truth” the character wishes to present to the outside world.
Deep third certainly isn’t just first with a change in pronouns.
Ann Laurel Kopchik 
Thanks for that bit of insight into deep 3rd. I am a novice working on my first piece of work which I am trying to put in Deep 3rd. Ran across this post in the search engine. It’s helpful to know that difference from 1st, which isn’t so obvious on the surface, but when you analyze the two, you’re absolutely right. Simply put, in 1st person – the person is telling you what they want you to know. In 3rd person deep, you have access to what’s going on in their subconscious mind.