The best overall product flying US to Europe is on Singapore Airlines in Suites. They fly once daily from JFK-FRA (SQ 25/26).
Absent that, the easiest product to find is Air France's La Premiere. Followed by Lufthansa First Class and then there's the rest.
If you're talking about Business, AA will have all-aisle access, all-lie flat on any of their widebodies, but I'd stick to the 787-9s (DFW-MAD, for example) or the 777s (advantage to the 777-300 (some DFW/LAX/JFK-LHR) but the refurbished -200s are nice, too. The service is hit or miss, and the food won't be as good as some of the other high-end European carriers (AF, Lufty), but it's more than edible.
If you're talking about Premium Economy, I just got back from a Beijing trip on AA and flew Premium Economy over there and Business back. Business is, of course, better, but honestly, Premium Economy was more than comfortable for the 14 hours I was on the plane. On a 9 hour flight to Europe, I'd be plenty happy. If you imagine a domestic first class seat, it will be a bit nicer than that (e.g. footrest, more recline), but otherwise comparable. I can't comment on any of the other airlines' premium economy except BA's World Traveler Plus, which I'd rate as comparable.
If you're talking about Economy, honestly, it doesn't really matter. Fly what's cheapest, but don't forget about bag fees, fees to select seats, etc. Those costs add up, and often work out to be more in total than if you'd just booked a full service carrier that provides free checked bags. I'd try and avoid any carrier that is 10-across on the 777 (3-4-3 config) or 9-across on the 787 (3-3-3). Delta is still 9-across on the 777, which makes them more or less the winner by default of the US airlines for the 777 flights.
Note that with many of the US airlines, they'll let you pick an extra legroom seat for free at the gate, but you'd have to pay for it at any point before then (including at check-in). It's worth knowing which of those seats are unassigned when you head to the airport; it never hurts to ask once you get to the gate. Another thing to pay attention to is people getting upgraded at the gate; chances are, they had better seats than you did (assuming you didn't pay for them) because they get the extra legroom seats for free.
At the end of the day, unless you're trying to fly in a premium cabin and experience lounges and the like, just try to get there as cheaply and quickly as possible. You'll likely be happier on United nonstop to London than connecting through Atlanta to fly Delta just to avoid a 10-across 777. You're taking a 9 hour trip and making it 12-13.
All that said, Lufthansa has self-pour JW Blue and many other 18+ single malts in their first class lounge at JFK. That was fun.