What's the difference between [V-ながら][V2] and [V-ている]間[V2] ?
For example, is there any difference in nuance between these 2 sentences:
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means that Mr Tanaka primarily does A. Incidentally, he also does B.
田中さんは、友達と飲みながら通常会話を学びます。 Mr Tanaka learns casual conversation skills while drinking with his friends.
The main action is drinking, it's the whole context. Incidentally, it's also the unrelated opportunity to practice conversation.
Some grammar books would tell you that "ながら" is similar to "のに", to show that it's linking two different actions, and does not concern time (even though they are simultaneous):
is almost "even though I'm watching the telly, I'm concentrating on my homework." It's a kind of opposition showing that the two actions are not logically connected.
This is the impression I get from the sentences:
Tom was studying for (at least) the entire time he was watching TV. He may have studied later too, it's unclear; but we can at least say that while he was watching TV, he was definitely studying. The sentence is interested in telling us what Tom was doing during the time he was watching TV.
Tom was studying while watching TV. He may also at some point have just watched the TV without studying, but this isn't important. The sentence is interested in describing (the nature of) Tom's action of studying and is not interested in when he was watching TV.
I've answered your examples rather than your actual question, I'm afraid. ^^; Perhaps someone else will be able to tackle it better?
Your example sentences sound pretty much the same. My preference is for the ～ながら version, since both actions share a subject and are volitional.
The main difference, I think, between these two forms shows up when we add a second subject to the mix:
○ トムは弟がテレビを見てる間勉強していた。 Tom was studying while his brother watched TV.
× トムは弟がテレビを見ながら勉強していた。 (incorrect)
The two actions in a ～ながら construction must have the same subject, so you can't use ～ながら to construct a sentence of the form, "Person #1 did A while Person #2 did B." ～ている間, on the other hand, merely means "While [action] is happening…" or "While [condition] is true…", so you can have different subjects:
雨が降っている間、このカフェでコーヒーでも飲みましょう。 While it's raining, let's grab something to drink at this coffee shop.
ねこがいない間はネズミは遊ぶ。 While the cat's away the mice will play.
I'm going to avoid the discussion of which is the primary action and which is the secondary; those kinds of rules tend to break down in everyday usage and don't contribute much to learning.