Is there any difference between using 다고 해도 and 아/어 봤자 in this translation?

Question

Right now I am studying 2 grammar points: 다고 해도, 아/어 봤자. It's been said that these 2 grammar points can be used interchangeably.

I wrote 2 translations for "Even though the grammar I studied is difficult, I will be able to use it well."

1. 아무리 배웠던 문법을 어렵다고 해도 제가 잘 할 수 있을 거에요.

2. 아무리 배웠던 문법을 어려워 봤자 제가 잘 할 수 있을 거에요.

Is it really true that these are interchangeable and there is no difference in the meaning of "Even though"?

Answer 1

I don't think so. Your first sentence sounds ok, but the second one doesn't sound right. If I may make the first one better though: "지금까지 배운 문법이 아무리 어렵다고 해도 잘 할 수 있을 거예요."

~아/어/해 봤자 can be used to mean "even though", but I think it has a nuance of "only so much". For example:

햄버거가 아무리 맛있어 봤자 콜라가 없으면 소용없다.
Hamburgers can taste good, but without cola, it's only so much.

해봤자야.
You could try, but you can do only so much. (it's little use)

싸다고 해봤자 10만원은 할 거 아니야?
Cheapest ones should cost like 100 thousand won as well, no?
(meaning that calling them "cheapest" means only so much)

So maybe that's the reason the second one sounds awkward? As I read

아무리 ... 어려워 봤자,

I am expecting to hear something that would a little bit nullify this. For example,

아무리 배웠던 문법이 어려워 봤자 앞으로 배울 내용에 비하면 아무것도 아니다.
Even though the grammar I studied is difficult, it's nothing compared to what I will study afterwards.
(= difficult it is, I might say, but it's only so much, because what I will study from now on is much more difficult.)

sounds OK.

Answer 2

On interchangeability, yes and no.

Yes in the sense that they mean the same thing (at least roughly). But no because 해 봤자 is often deprecating. This comes out clearly in the familiar expression:

뛰어 봤자 벼룩이다. ('Though [null-subject] jumps, [null-subject] is a flea,' or 'Let it jump ever so high, a flea is still a flea'--said of someone's futile effort particularly in flight but also more generally.)

You may want to stick to 한다고 해도 or 하더라도 until you get the exact nuance of 해 봤자.

Apart from that, your sample sentences have some issues. '문법을 어렵다고 하다' is 'to call grammar hard'; so you'd need someone to do the calling, as in '사람들이 문법을 어렵다고 하다' meaning 'for people to call grammar hard' (or 'People call grammar hard'). Otherwise I believe what you want is: '문법이 어렵다' meaning 'grammar is hard.'

Also 'grammar you learned yesterday' is '어제 배운 문법.' '배웠던' will suggest cessation of learning. For example, grammar might have changed, or it's been a very long time and you've forgotten. '우리가 어렸을 때 배웠던 주산을 이제는 아무도 배우지 않는다.' ('No one learns counting on an abacus as we used to do in our youth,' or literally 'the counting on an abacus we used learn when young, no one learns anymore.')

Thus we get to '배운 문법이.' But this standing alone sounds very strange. I think here the absence of a definite article (something not available in Korean) is making a difference. Korean will find some alternative way of limiting 'learned grammar'; for example, (borrowing from the other answer) '아무리 지금까지 배운 문법' or '아무리 어제 배운 문법이.'

Last, I don't think '문법' can mean a 'bit of grammar.' Imagine saying in English, 'Though the linguistics we learned yesterday is hard...' This sounds like one kind of linguistics as opposed to another, not this bit in linguistics as opposed to that.

Putting it all together you might want:

아무리 어제 배운 것이 어렵다고 해도 저는 잘 할 수 있을 거에요.

Here 저는 is preferable to 제가 because the 아무리-clause suggests the thing being too hard for some people though not you.

If you have to have 'grammar' in there:

어제 문법 시간에 배운 것이 아무리 어렵다고 해도 저는 잘 할 수 있을 거에요. (Even though what we learned yesterday in grammar--literally grammar hour--is difficult, I will be able to do it well.)

Contrast that with wanting to belittle your opponent by saying:

네가 아무리 열심히 연습해 봤자 나를 이길 수는 없어. (No matter how hard you practice, you cannot beat me.)