After more than a decade of crossing the Atlantic out of Logan, I can tell you that Hamburg remains one of the more refreshingly uncomplicated business class puzzles in the transatlantic network — mostly because there's no nonstop option, which forces a more interesting routing decision than travelers expect. There is currently no direct service between the two cities, so business class from Boston to Hamburg means connecting, typically through Delta and Air France-KLM's joint venture partners via Amsterdam or Paris, through American via London Heathrow or Philadelphia, or through Lufthansa via Frankfurt or Munich. My preference leans toward Lufthansa's Frankfurt connection, since the airline is progressively rolling out its new Allegris business class on select long-haul aircraft, featuring suites with closing doors on certain configurations — though note that Allegris availability is still limited and route-dependent, so it's worth checking your specific aircraft type before booking. American's transatlantic segments, meanwhile, benefit from its 777-300ER and 787 business class flat-bed seats, particularly strong on the Philadelphia routing given the airline's dominant hub presence there.
The insider move that most travelers miss: routing through Munich rather than Frankfurt on Lufthansa often yields both a smoother connection and a better shot at newer aircraft, since Munich has become something of a proving ground for the carrier's refreshed long-haul fleet. Whichever hub you choose, build in at least 90 minutes for European connections during winter months, when Frankfurt and Amsterdam both experience deicing delays that cascade through the morning bank of arrivals. Hamburg's own airport is compact and efficient, with immigration rarely taking more than 15-20 minutes even on full widebody arrivals.
January through March, then again in October and November, consistently produce the softest fares on this corridor, as Hamburg sees relatively light American leisure demand outside the summer trade fair season. Given how much routing and aircraft type can shift pricing and product quality week to week, I'd strongly recommend setting up fare alerts rather than checking manually — the sweet spots on this route tend to open and close faster than most travelers anticipate.