BA is currently operating 757s to HEL, is scheduled to operate 319s mid next year. Flights will be from T3 whether BA or AY.

I'm not sure about conflicting reports, I think the message is quite consistent:

BA offers better seating (standard 2-3 CE seating), great (usually) crews, decent meal.

AY offers terrible cramped no-legroom 3-3 seats (with the middle seat blocked), nice (although somewhat "cold") crew, better food (more, better quality, with a Nordic twist).

Choose BA if you value more spacious seating and you like the BA crews. Choose AY if you want to try something different and want the better catering.

Timings may play a role, the first BA flight to HEL is at 1230, while AY has departures at 0730 and 1020. If you arrive from DXB on BA106 at 0620, I wouldn't suggest hanging around till 1230 (you have no access to T5 departure lounges, only the Arrivals Lounge, assuming you don't need a visa to "enter" the UK). The 1020 AY flight is timed fine for that connection. Bear in mind you can book this as a BA 6032 codeshare if you want the extra status miles.