No it is not the case like this.
In order to trigger the partner availability link, you have to hit a date where BA has not availability. Then you can change your dates by 7 each time and you will see both BA and OW. Play a little bit with the search engine and when you learn how it works it is very nice. Has some bugs though.. sometimes just doesn't work, I usually log out/in again and it works.
I would go for AY, I don't have experience but for some reason i believe that they will have great product. Also HEL airport has good reviews for easy transferring. If they also have personal tv screens like BA does would be nice.