It's completely wrong to suggest you can't have a good home life at BA.
For starters I spend FAR more time with my family than most people who work normal 9-5 (read 8-6) jobs. Anyone who works in the City is lucky to see their children at all during the week. At least that is certainly true for the people I know who are travelling out to the commuter belt every day.
Specifically in relation to easyJet vs BA, I would question the amount of "quality time" you are getting at home on a block of work at easyJet and therefore the relevance of being home every night. When I did it (at LGW) I remember a) not being able to make any plans for downtime on "days on" anyway because my roster would always change and b) being close to useless after coming home off early duties anyway. I accept it might be better at regional bases.
Let's be honest, whether it is coming home at 2am and crawling into bed when everyone else is asleep already, coming home at 2pm and falling asleep on the sofa, or being 4000 miles away in a hotel, the life of an airline pilot has it's challenges from a family perspective. It's just which of these challenges you find easiest to live with that matters.