I thought I read somewhere that Boeing purchased an Airbus A320 so it's engineers could take a look at it and... ehm.. "learn" about the competition.
I don't recall hearing any similar stories about Airbus purchasing a B737... besides, the A320 completely rapes the B737 on longer-range missions, the B737 has lost its advantage as it's got heavier, which sucks... but no amount of whining will make it suddenly better. The NEO/MAX will only widen this gap because the NEO will have a larger diameter fan than the B737 (that helps with efficiency) but the B737's will be lighter which will make it better for shorter-range. Really, Boeing should've upgraded the B757, shortened it to take the 180 seat market and kept the B737 for 130-150 seats keeping it light and simple.
But then I love the B757, so I'm a little biased
That's true Boeing has been known to buy old aircrafts used by various airlines. They somehow buy the plane in exchange for a plane from Boeing and then they put the plane into the leasing market. Because Airbus and Boeing has leasing companies too. Here's one comment from a website
"
For eg. Boeing is reported to have offered an Asian carrier shortened 777's in exchange for their old A310s. I am not sure of which airline.
But I don't think, Boeing takes the aircraft for studying them or anything. The old A310's would be put on the lease market. The idea essentially is to 'break-into' a customer who would otherwise go for the other mfr. In this kinda deal, the airline is freed from the hassle of searching for a buyer for the old planes.
There is a rumour about Indian Airlines getting a similar offer from Boeing for the replacement of its 273 seater Airbus A300's.