My opinion is based on having logged 1897 hrs. in the Phantom (178 combat missions in SEA from Korat Thailand and a tour at RAF Lakenheath), a flight in the Lightning at Coltishall in 1973, 525 hrs F-15A/C , 260 hrs. in the F-14A, and 223 hrs. in the F/A-18A (Navy exchange tour with VX-4).
Now one flight in an aircraft is not nearly enough to really know how an aircraft will do in an engagement but I will say that the flight controls in the Lightning were much more harmonized than those in the Phantom. And although I never had a chance to go 1 V 1 with a Lightning in a Phantom, I believe I would have tried to keep the Lightning from getting a shot and try to run him out of fuel. One of the problems is that we very seldom flew the Phantom without wing tanks, which did not give a good understanding of its true capabilities (and fuel limitations). In combat we did not hesitate to jettison those tanks when any MiGs were around.
First to the OP; realize that the focus of modern fighter tactics is to try to kill your enemy before you get to the merge. In that case the on-board systems are the key. This includes the ability to identify the target at beyond visual ranges. The F-15C has at least two systems that allow BVR ID. This is especially important in a situation where you do not know how many enemy aircraft are against you. That is also why you can’t get a true picture of an aircraft’s abilities (or your own) when you are doing 1V1 or 2V2 training missions. In those instances you know that when you have the one or two aircraft accounted for you don’t have to worry about some other bogy ruining your day. Hence, when the training mission is a Red Flag, and the number of aircraft is not known, you learn very quickly not to get into a very long turning fight.
Going to the F-14 from the F-15 was a step down in my opinion. The thrust to weight of the F-14 was about the same as the Phantom, and although the swing wing allowed better low speed handling in the F-14, it also allowed you to have a pretty good idea of the F-14 energy state. Also, although the Phoenix missile was a long range weapon, it weighed 1,000 lbs. and was not very maneuverable. So against a fighter target you had to hope the target was not aware of the launch and did not acquire the missile as it was fairly easy to out maneuver it. I never had a chance to fly the F-14D with the GE F110-400 engines which I understand was a much better aircraft than the F-14A.
So to cut to the chase, I agree with Courtney, of the aircraft listed I would pick the F-15 to go to war. By the way my next pick would be the F/A-18. Unfortunately the best F-15 out there is probably the Singapore F-15SA with F110-GE-129C engines, the AN/APG-63v3 AESA radar, an Infra-Red Search and Track, and the JHMCS helmet-mounted display.
Also, while I was at VX-4 we had two RN exchange officers there; Dave “Brave” Braithwaite and Clive “Spag” Morrell. It would be interesting to get there view of the Harrier vs. the F-14.