1. “But even my own parents won't be able to tell which soldier is me!”

2. “But even my own parents won't be able to tell which soldier I am!”

QUESTION: Is this "which" a conjunction or a determiner here?

ANSWER: The word "which" is a determiner in the noun phrase "which soldier".

Your sentence #1 could be parsed as:

1. “But even my own parents won't be able to tell [which soldier is me].”

Embedded in that sentence is the subordinate interrogative clause: "which soldier is me?" And so, the sentence could be paraphrased as: But even my own parents won't be able to tell the answer to the question "Which soldier is me?"

For your sentence #1, if we extract that subordinate interrogative clause and treat it as a main clause,

• "Which soldier is me?"

we'll see that the noun phrase "Which soldier" is the subject of that clause, and so, the word "which" is the determiner of that noun phrase.

Now, with the above in mind, we can convert your original sentence #1 into your original sentence #2 by using a slightly different subordinate interrogative clause, one that would correspond, more or less, to the two below main clauses:

• a. "I am which soldier?" -- [interrogative phrase in situ]

• b. "Which soldier am I?" -- [interrogative phrase fronted, and with subject-auxiliary inversion]

To see this, let's embedded what would basically be that #b version into your example, and we'll get the below:

3. “But even my own parents won't be able to tell [which soldier I am].”

Notice that the subordinate interrogative clause, which corresponds to the main clause "Which soldier am I?", does not have subject-auxiliary inversion. That's because subordinate interrogative clauses will front the interrogative phrase (when the interrogative phrase isn't the subject) but not undergo subject-auxiliary inversion (well, usually it won't).

That last version #3 is identical to your original version #2. (Well, other than the omission of the exclamation mark.)

Now as to the usage differences between your #1 and #2 versions: version #1 would be the usual version used, as it would be used in neutral and informal situations; while version #2 would often be thought to be sounding rather formal and stiff, and so, it would be used in a more formal style.

This is an interesting question. I would say that the two options are functionally equivalent. By that, I mean that they say the same thing, but in different ways. But yes, I'd say that either is perfectly acceptable.

The denotative difference is that the soldier is the subject in "which soldier is me," and "I" is the subject in "which soldier I am."

I imagine the first--and I'm a programmer so this probably stems from that--as something like this: you're looking at each individual soldier and saying "is this him?" and not being able to tell. In the latter example, I picture it more as looking at the whole entity of soldiers at once and trying to pick the speaker out. Those aren't denotative at all, but they're ways to visualize the tone with which I read each phrasing.

Again, the result is the same, but the first way of saying it--the one that you originally asked about--puts more of an emphasis on the difficulty of identifying the speaker, by somewhat depersonalizing the statement inherently. The speaker will have lost his identity so much, that even talking about it causes him to speak in terms of the soldiers and not himself.

I hope that makes some sense. That part is super subjective and another answerer may well read it differently, but as far as the objective part is concerned, yes, either is correct.