By "Big Company Experience" I mean guys who have time flying for BA/Cathay on Big Jets etc. but haven't got a whole heap of command time on said aircraft.
If your trying to say you need Heavy jet time to get an interview then; BOLLOX Those hours would certainly make you VERY competitive but they're hardly the benchmark... its not like NZ is hiring DEFO's on the 777.
There are PLENTY of LINK Co-pilots who have left for Big Bro in recent times so get those updates in.