as bescobar said, if you can get into J, that's the way to go.

I've done very similar routings as yours (JFK to BKK somehow) several times in both DL and KE and I'd go KE all things considered. It's a bit more gracious in Y except that they will wake you up and make you put your seat up during meals. But the service is generally pretty good and they'll get you anything you ask for in terms of drinks & the like.

The big problem, however, that I ran into was getting choice seat assignments - even being PM at the time, I was always quite near the back of the bus. Don't know if the seat assignment methods have changed since then - but you'll have to call KE direct to nab a specific one and I think there is a time-frame for that.

I did one trip in J on DL metal (from ICN to NRT to JFK) once and it was quite nice on both legs. Am currently in SYD from a trip in KE J and it was fine except the seats aren't full lie-flat, so they're not the most comfortable. Am returning on the A380 and am looking forward to that. But if I could have done J in DL, I would have over KE.

My $0.02

Let us know what you choose and how it went.