I have flown Asiana a couple of times, west coast to Korea, and Korea-Japan. I caveat this by saying that it was a few years ago, so things have probably developed a lot.
They definitely weren't too bad (in economy). Food was very Korean (but I like that), planes were newer, service was adequate, if not "warm". The prices couldn't be beat then, so no real complaints.
I don't think that they have any major safety issues (certainly no crashes that I can recall in the last few years), and I'm sure they've probably brought their service standards up to meet competition.
Then, they did not have PTVs in economy, but that was with 763 and 747 combis - I'm sure they've probably implemented them by now.
The only negative I remember is that the seat pitch was rather tight - probably 31" ~ 32" - but that's not too extreme.
Be curious if you take them to hear a trip report...
Best regards from London.