In the last few years I've had very good experience on JET, Lufthansa, United, and Swiss. Coach for

My husband and I are preparing to book our flights to Europe for our honeymoon. We are still undecided on Business or First Class. Which domestic U.S. airline is the most comfortable and accommodating for international travel?
That's like asking "What restaurant in the world serves the best pizza?" Everyone will have their own opinion, there will never be a consensus. However, to get lots of opinions, you may want to go over to Flyertalk.com , as the travelers there will likely have a thread to exactly this question.
As to the 'best', one cannot generalize as it may very well depend on the route, and therefore the planes used on that route. Your domestic US choices are limited to UAL, Delta, AA, and USAir, none of which shine in my book. With the 2 big mergers in the past few years (Delta + NWA, UAL + Continental) you could be flying on an antiquated B767 or B757, or A330, or a brand new Boeing or Airbus.
In the last few years I've had very good experience on JET, Lufthansa, United, and Swiss. Coach for me, unfortunately. Airlines are regularly updating their business class seats to be competitive, and very few airlines fly first class transatlantic any more. I did get upgraded travel silk road to biz class on Jet in 2010, and that was superb. Better than anything I've seen on any other airline.
I would opt for biz class IF the seat is a true lie-flat travel silk road bed seat. UA has these on some (not all) of their trans-Atlantic flights. If the seating is barca-lounger type seats in biz, I would consider first class. For me, personally, the BEST choice will be the one on which I can lie down and sleep on the way there! I do not sleep in economy reclining (NOT) seats.