Boeing was first. They established them selves as the strongest brand, and Airbus had no points of difference to push Boeing off their throne. Boeing was used almost exclusively for decades; until recently when a $9.5 billion order on Airbus planes was made – sheduled to overtake Boeing in the long term.
So what has happened here? Boeing had trouble with their most popular model (the 787) and when they could not deliver, nor seemed as appealing as before due to trouble with batteries etc. they lost their points of parity – a plane has to work – and thus lost a significant market share in the Japanese market.
In the world wide market, Boeing and Airbus aim at the exact same market, which could be considered too broad of a market – which is not a profitable idea. One example of this is “But Boeing’s strategy calls for it to be dominant in the sales of midsize and larger jetliners because Airbus has pulled ahead in sales of the newest single-aisle planes, with the A320 neo tallying more advance sales than Boeing’s 737 MAX.” To avoid this, Boieng needs to create a different point of parity, for example the Boeing 777X’s fuel-saving abilities.