虽然 and 尽管 can both be translated as "despite" and "although". I've been familiar with 虽然 for a longer time already but I recently came across 尽管 for the first time. Is 尽管 a more formal or poetic term? In what contexts would you use 尽管 rather than 虽然?
Let me translate an answer I saw on a Chinese website.
尽管 and 虽然 are somewhat different. "尽管" implies personal opinion (similar to "although"?), indicating that the speaker understands that the situation usually leads to result A, but insists on result B nevertheless. "虽然", however, does not carry this connotation because it goes with 但是 and can be treated as "but". "虽然" merely states a fact.
When used as conjunctions, 尽管 and 虽然 are synonyms.
However, 尽管 can be used as an adverb to mean feel free (to do). 虽然 does not share this meaning. For example,
尽管 Can be used as adv. and conjunction in Chinese.
When it is an adv..it's different from 虽然. It means without constrains, can do something freely.
Eg. 你有什么困难尽管对我说。(just tell me, if you have any problem.) 你尽管来吧。（just come)
When it is an conjunction, it functions like 虽然。and most time it is ok to substitute one with the other.But,in my opinion they have little different in pragmatic.
虽然 leads a turning clause.
他虽然身体不好，可是仍然坚持工作。in this sentence, "身体不好＂should be the old information,and "坚持工作＂should be the new information. ----he got sick these day,right? So pity.. ----yes, 他虽然身体不好，可是仍然坚持工作。
尽管 leads a concessive clause.
他尽管身体不好，可是仍然坚持工作 in this sentence, "坚持工作" should be the old information,and "身体不好 "should be the new information. ----I heard that he is workaholic. ----yes, 他尽管身体不好，可是仍然坚持工作。 Coz here we may say 他还是会坚持工作的，尽管他身体不好。
I'm going to keep it simple...
IMO, it's extremely helpful to understand the meaning of each character in a phrase, rather than just the phrase itself. This will help you break down the meanings of characters, and will help your understanding of subtle differences, as you're asking here.
So... Taking an excerpt from gonnastop's post:
"Thus, when you are expressing strong personal opinion, 尽管 is a better choice."
If you look at what 尽 means... it means "strong, utmost, to the end, exhaust". And, 管 means to "take care of, to care about"
So you can conclude that a phrase with the word 尽 would most likely be a stronger version of that phrase. This can help you think about the individual meanings of characters, and explain these nuances.
I give another similar example in my post here: Difference between 最高领导人 and 主要领导人之一?
Concessive clauses belong to a category of contrast clauses. They usually denote some obstacle which does not prevent the fulfilment of an action expressed in the main clause. The first word that introduces the contrast clause is called a subordinator.
Both 尽管 and 虽然 (in the context of the question asked) are concessive subordinators or subordinating conjunctions possessing the English meaning of "even though" and "although" respectively. To answer the question, 尽管 (or even though) is emphatic while 虽然 (although) is not.
The following examples show clearly the distinction between the two words:
(Here, 尽管 is used to highlight to readers the extraordinary risk that the firemen faced.)
(Here, 虽然 is used because the obstacle is certainly not something out of the ordinary and does not need emphasizing.)