They are conjunctive particles and mean “even though“, but there is a slight nuance.
“のに“ is used to express the contradiction between two things based on the fact and it indicates your surprise, confusion, disappointment, or complaint.
“ても“ is used in the same way as “のに“. “ても” sounds less emotional than “のに“ but it depends on the context and your facial expression. “ても“ is also used to explain hypothesis.
ネイティブのように、日本語を話せるようになりたい。
[NG] (どんなに)時間がかかるのに、絶対に諦めない。
[OK] (どんなに)時間がかかっても、絶対に諦めない。(hypothesis)
- Ken: We have only 30 minutes left to head to the party. We should be done for the day! And we have to go to the party venue.
パーティーまで、あと30分しかない。今日はもう(仕事を)終わりにして、会場に行かなきゃ。 - Leo: Hmm, do you think I will have to go even if I’m busy?
[OK] んー、忙しいのに、行かなきゃいけないのかな?
-->It indicates that he isn’t satisfied with going to the party.
[OK] んー、忙しくても、行かなきゃいけないのかな?
-->It indicates that he is just wondering if he should go to the party. - Ken: Yes, it’s the most important annual event in our company. You know all employees have to attend. So even if you were the CEO, you would have to be there.
うん、うちの会社で、最も重要な年次行事だからね。社員全員が出席しなきゃ。
[NG] リオが社長なのに、行かなきゃ(いけないだろうね)。
[OK] リオが社長でも(or社長だとしても)、行かなきゃ(いけないだろうね)。(hypothesis)
- Meg: You saw Miki with someone yesterday, right? Do I know that guy?
昨日ミキが誰かと一緒にいたんでしょ?私が知っている人? - Amy: Um...you should hear it straight from the horse's mouth.
んー、ミキから直接聞きなよ。 - Meg: Why? Although you knew it, you’re not going to tell me. You’re so mean!
[OK] なんで?知っているのに、教えてくれないんだー。意地悪だな!
-->It indicates that she is disappointed with Amy’s attitude and complains about it.
[OK] なんで?知っていても、教えてくれないんだー。意地悪だな!
-->It indicates that she is just disappointed with Amy’s attitude. It’s less emotional than the above one.