I saw a post circulating claiming that these two grammar points are interchangeable, and I’d just like to take a second to say: no, they’re not.
-는데도 can be thought of as a the abbreviated version of -는데 그래도. With this in mind, we know that the result in the second clause following -는데도 is contrary to what we would expect based on the information in the first clause.
나는 주연 씨를 매일 만나는데도 친하지 않아요. I meet Ju-yeon every day, but we’re not close. (Even though I meet Ju-yeon every day, we’re not close.)
From the first clause, you know that I meet Ju-yeon every day, and following that, the logical assumption is that we’re close. However (this is where 그래도 kicks in), the truth is that we’re not close at all. The information in the first clause has no bearing on that in the second.
방을 하루종일 청소했는데도 아직 더러워요. I cleaned my room all day, but it’s still dirty. (Even though I cleaned my room all day, it’s still dirty)
열심히 공부했는데도 시험에 떨어졌어요. I studied hard, but I failed the test. (Even though I studied hard, I failed my test.)
-더라도 is similar in that the information in the first clause has no effect on the information in the second clause. However, with -더라도 we are working with a hypothetical scenario.
약 맛없더라도 꼭 먹어야지. Even if the medicine tastes bad, you should take it.
In this sentence, we don’t know what the medicine tastes like, presumably because it hasn’t been taken yet. However, regardless of whether it tastes good or not, the speaker is advising that the medicine must be taken.
방을 하루종일 청소하더라고 더러울 거예요. Even if I (were to) clean my room all day, it’ll be dirty.
열심히 공부하더라도 시험에 떨어질 거예요. Even if I (were to) study hard, I’ll still fail the test.
When used in the past tense, -더라도 has a feeling of inevitability when it comes to the final outcome: regardless of whatever past action taken, the result would remain unchanged.
방을 할루종일 청소했더라도 아직 더러웠을 거예요. Even if I had cleaned my room all day, my room still would’ve been dirty.
열심히 공부했더라도 시험에 떨어졌을 거예요. Even if I had studied hard, I would’ve (still) failed the test.
Again, we can see that the information in the first clause of the sentence has no influence over the result in the second clause of the sentence.
The difference between the two grammar points can be summed up thusly: -는데도 can be translated as “Even though”; -더라도 as “Even if”.
I hope this post helps to sort out any confusion!