More info needed
Rex.
You're wanting to know what easyJet has over BA.
Stable roster is a starter. Being able to be based somewhere other than London is another.
You haven't elaborated on your resident situation. Do you live 10 minutes from LHR, and would your family be happy to relocate for another job? Have you even enquires about part time, or flexible working due to your children's age?
I know of a huge number of people in both airline and corporate aviation, and lifestyle is the number one issue. What I get as an undertone from your post (and forgive me if I'm wrong), is that you want something different but don't actually know what you want, and are not prepared to take a drop in income to achieve a better home life balance.
For me personally, I have always looked at the time at home as opposed to the financial income aspect. Rotations, rosters and leave allocation is all that matter to me. Would your wife and children complain if you went to work and were gone for 2 weeks, only to be at home not thinking about aviation for the next 2 weeks. If you have teenagers, then most likely they're not bothered if you're there one day to be next (to your face), but don't under estimate the 'coming home every night' part of low cost operations, it really is worth some of the crap you have to put up with.