I can't fully compare the quality of the different business class options across the Atlantic. However from a pricing, and logic of connection there is no doubt I would take the AA option.
6 hours is not much to visit Moscow, SVO is a good bit of way from the city, and traffic can be horrendous in Moscow. I think there is a train, but I have never looked in to the details of that. Depending on your passport, but most nationalities would need a visa to enter Russia.