EF2000 was designed for air to air combat in the ECM/threat heavy central European enviroment, the RAF pushed for, and got, more fuel capacity for UK airdefence.
But in service it will be swing-role, with a formidable weapon load. The RAF will operate it mainly for air-to-air, but will have a couple of squadrons for air-to-ground.
JSF came out of the wreckage of the cancelled US programmes of the early 90's, A-12, NATF, MRF, designed to replace aircraft such as the A-6, F-18 F-16 and F-117. It reflects the reality of post cold war defence spending.
With new technology, it was decided to add a VSTOL version for replacement of the USMC and RAF/RN Harriers. That got the UK on board, (the high cost and limited market for a new VSTOL aircraft, plus the technical problems and limitations of previous 'advanced VSTOL' studies has been a problem since 1965, when the UK cancelled the P.1154 supersonic VSTOL aircraft).
Sounds like a dog's breakfast of a specification, but the F-16 started out as a technology demonstrator, and look how successful that's been. If it can deliver, it will be a formidable, versatile machine, and affordable enough to buy in decent numbers. But JSF is unlikely to be available before 2012 for export.
So different aircraft for different requirements, and the two aircraft will eventually fight it out in the market.
Larger services such as the RAF will have room for both.