I flew this route for the first time last month, so a healthy sample of one to go on.
I took AY in both directions, in Y. It was half the price of BA. Shiny 350 out and a scabby 330 back, but an exit seat with loads of legroom each way. Great lounges: CX at T3 and AY at HEL. I was surprised to get a free drink on-board.
Given I'm unlikely to fly J on this route, I'm just as unlikely to fly BA based on my experience.