If ease of connection is a critical part of the decision, Finnair would be your best bet, in my opinion. Finnair uses the AA terminal at JFK. HEL is relatively small and you won't have to make any terminal changes there. If you go via London, you'll have to change from Terminal 3 to Terminal 5, which is a pain in the neck. Madrid is a fantastic airport, but you're adding about 1000 miles each way to your trip over a Helsinki connection. While Madrid would likely have fewer weather problems in the winter, Iberia seems to be constantly embroiled in a labor action, and this may only get worse with the prospective BA merger on the horizon.

There are great arrivals lounge facilities with showers in London and Madrid. I haven't seen them Helsinki, but they may exist in one of the Finnair lounges.

As far as service is concerned, I"ve flown AA, IB, and AY on transatlantic routes in the past year and I can't tell that one is significantly better than another. As a previous poster noted, if you can snag a BA Club World seat (by connecting in Canada), that will likely be your best transatlantic service. Within Europe, BA, IB, and AY seem equally mediocre in "business class" to me.