By what measure is it a much smaller company? By planes sold it appears negligible: between 2007 and 2016 Airbus delivered 5,644 and Boeing delivered 5,718, for a difference of 74. In terms of market share they're roughly equivalent in twin-aisle jets and Airbus has a significant lead in single-aisle jets (for obvious reasons).

Reality doesn't downsample when you're not looking at it, your eye does that.