Wasn’t the Boeing offering pretty much superior in every way other than looks?
apparently not, says wiki
Arguably the most persuasive demonstration of the X-35’s capability was the final qualifying Joint Strike Fighter flight trials, in which the X-35B STOVL aircraft took off in less than 500 feet (150 m), went supersonic, and landed vertically — a feat that Boeing’s entry was unable to achieve
…
When near to the ground, the Boeing X-32 suffered from the problem of hot air from the exhaust circulating back to the main engine, which caused the thrust to weaken and the engine to overheat
The United States Department of Defense officials and William Bach, the UK Minister of Defence Procurement, said the X-35 consistently outperformed the X-32, although both met or exceeded requirements.