If you choose a JFK-SFO flight operated with a 767-
323ER / 763 (two class service, not the 767-
223ER / 762 a three class service,) you will get the "NGBC" (the term to use for your search - including quotation marks).
JFK
can be congested, affected by weather, etc. (as can SFO) - but it's a nice flight with the product more often found on AA international service. Only you can decide whether it's worth the extra time, etc.
If it is not, maybe JetBlue for you, if you don't mind OAK or SJC.