I will make it short:
If you're flying Y then go for LH.
When flying J try DL.

Yes, DL does status matches for overseas customers. Wait untill you reached SEH on LH, DL will then comp you to Gold, their mid-tier medaillion level.
When looking on the FF programms DL wins by far after the M&M "enhachments" in august, except when you usually flying paid F / J.