Concession (Even Though / Although / Despite)

Telling a story where the outcome was not what anyone expected.

～ところが vs ～くせに: Use ところが. It is narrative surprise and passes no judgement on anybody. くせに carries open contempt for the subject (知っているくせに教えない), so it turns a plot twist into an accusation.

Something is more, or less, than its circumstances would lead you to expect.

～わりには vs ～といっても: Use わりには. It measures the outcome against a standard the first clause sets (安いわりにはおいしい). といっても does something else: it walks back an overstatement you just made ('though when I say X, I only mean...').

Formal writing, reporting an outcome that ran against the conditions.

～にもかかわらず vs A。それなのに B。: Use にもかかわらず. It is neutral and carries no feeling about the mismatch. それなのに is spoken and openly aggrieved, so it reads as the writer complaining rather than reporting.

The outcome contradicted a specific prediction, expectation or policy.

～に反して vs ～にもかかわらず: Use に反して. It needs something to run counter to: 予想に反して, 意図に反して. にもかかわらず only says the outcome held in spite of a circumstance, without naming anything it contradicted.

Conceding a point you just made, then qualifying it.

～とはいえ vs ～といえども: とはいえ is the workable formal one: it accepts what was said and adds the caveat ('that said'). といえども is classical and emphatic ('even X, of all things'), so it overstates an ordinary qualification.

Someone acted against the state they were in.

～ながらも vs ～とはいえ: Use ながらも. It pairs a state with a contrasting action taken anyway (狭いながらも楽しい我が家), so it attaches inside the clause. とはいえ joins two sentences and cannot bind a state to an action that way.