EK for sure. Take the money and an upgrade and do your 5 years. Be way ahead of where you would have been in BA, plus have international 777 PIC time within 5 years as well as a lot more money.
Then leave EK and use that experience to join a European operator and get the lifestyle, labour law protection, QOL and so forth. BA is 20 years to command plus a lot less money and things are going downhill there fast...