If it is your ambition to fly for BA, to fly long haul, or to fly the flag, then BA is the place to be and I wish you all the luck in applying.
Don't leave easyJet because it is such hard work. If you think five earlies are though, then crossing twelve time zones a week will definitely kill you. If you moan about all those night stops in LGW, well...you ain't seen nothing yet!
Don't leave easyJet for a better career. Career wise in BA you'll be in the same position as you are now, only 10-15 years later, flying the same short haul from the same left seat, in the same aircraft, through the same European skies. You'll be much older though.