Unfortunately AY is not a good choice when travelling from US to Vienna. The flight leaves HEL at 8:25 (3 days a week) and the JFK flight arrives 8:50. 4 days a week the flight leaves 17:25 which doesn't make it very fun either.
Finally, AY does not offer Business Class on the HEL-VIE route (for some unknown reason).
I would guess that AA/BA is your best choice. Sorry!