On the topic of F-15E vs. the Eurofighter...
IMHO, if the Eurofighter CAN'T beat the Mudhen BVR or WVR, there's something seriously wrong.
The Eurofighter has more advanced avionics (although I'm a bit suspicious of the capabilites of the ECR.90, but give it the benefit of the doubt), and the planned Tranche 3 ones get some nifty stuff like the full DASS (one truly promising defence system), helmet mounted display, and the PIRATE sensor (integrated FLIR/IRST).
I'm not sure about this next point, the F-15Es can carry AMRAAMs, but do the Eurofighter get their Meteors, which outrange the AMRAAM and has better electronics to boot? If that's the case, the Eurofighter then has the slightly better lance and the somewhat better shield. It won't be all one way traffic, but it won't be totally fair either.
I'd say it's quite like pitting a F-16 Block 30 against a F-4J Phantom, one with the AMRAAM and the other with the AIM-7M.
Summary: the Eurofighter should take it.