They were actually competeing for the F-16 replacement as a multi-role fighter aircraft. Though, with VTOL capabilities I can see why they would be considered a Harrier replacement.
They had a special on Discovery some time back showing them actually testing them through the various trials. The Boeing couldn't even try out for the VTOL test because it weighed too much, so had to strip it beforehand and this limited it's air speed due to exposed areas. When they landed, they just did a standard runway landing. The Lockheed on the otherhand did a vertical take-off, broke the sound barrier, came back and did a vertical landing no problems. Needless to say, they were the clear winners and got the contract.