I’m constantly getting mixed these two grammar points.
Is there some difference I can distinguish them?
といっても = “although [someone] says that, (actually it turns out not to be like that)”
とはいえ = “although that may be the case, (there is actually more to it than that)”
This is how I understand the nuance although I also believe they are largely synonymous but I do hear といっても an awful lot more. Please take all of this with a massive grain of salt as it is based on my own limited experience.
AFAIK they are synonymous and basically interchangeable. I think the only big difference is the degree of formality/contexts they are used in, with とは言え being more formal/used mostly in writing. I think Bunpro is just not coded in this instance to warn you that they want the more conversational phrase that they’re looking for.
“前のことから想像・イメージすることとは違って、そんなに程度が大きくないと修正・限定したい時に使う。”
From the bunpro hint alone it’s hard to tell what is to be inputted, but based on this website it seems like the biggest difference is that といっても corrects an expected value based on the first part of the sentence. In this case, my bag is heavy (and from this statement alone, only my bag is heavy), but your bag is heavier (thus correcting the “assumed” values of other bags implied in the first sentence).
I think when you see words that indicate a comparison of values like this もっと, といっても is used more often, while とはいえ can really be applied to any two phrases that contradict each other
“彼は吸血鬼とはいえ、まだ僕の兄上だ!”
Not really any identifiable or measurable quantity here, just two truths
… 多分
といっても can be interpreted as “even if x is said”, which is actually what the hint tells you. If you go by it alone you should have no trouble choosing the right one (I don’t know how does the hint for とはいえ look like).
The “even if” is my go-to translation of any form of と~ても pattern as I feel like this is actually what it means and is the most intuitive for me.