Developed with different roles and different weapon fitouts. F14 was an aircraft developed to carry the Hughes APG 9 and Phoenix AAM to keep the Soviet anti ship carrier killers from reaching weapons release range - not developed as a 'dogfighter'. F15 is more the classic air superiority aircraft.
One on one who would win? Back in the 70's initially the F14 may have had the drop on the F15 due to the range of its weaponry, but in a closer engagement the F15 would be the more manoureverable. It would probably come down to tactics, pilot proficiency and weapons.