The F-20 was called the tigershark if I am not mistaken. It was developed by to compete against the F-16. The F-16 won mainly due to the avaliability to use the same engine as the F-15, which was already in service.
The F/A 18 is not the same type of air superiority fighter as the F-14. The role of the F-14 was strictly air-superiority, until recently when it was reconfigured to a limited attack role.
Make no mistake, the F/A 18 is a dog that can hunt with the use of Amramms, sidewinders, and a 20 mm vulcan cannon. It does not have the range or speed potential of the F-14 but it is more maneuverable and better suited to the attack role. The US is simply attempting to get a multi-role platform in place for the Navy.
One of the main advantages of the F-14 was its ability to use the Pheonix missile system. This system was designed to shoot down long range bombers out to 100 miles.