The RAF Typhoon, formerly known as the Eurofighter, should nonetheless have been vastly superior in air-to-air combat whether BVR or close in within visual range (WVR). The cripplingly expensive, long-delayed Eurofighter was specifically designed to address the defects of its predecessor the Tornado F3 – famously almost useless in close-in, dogfighting-style air combat. The Typhoon was meant to see off such deadly in-close threats as Soviet "Fulcrums" and "Flankers" using short-range missiles fired using helmet-mounted sight systems: such planes were thought well able to beat not just Tornados but F-16s in close fighting, and this expectation was borne out after the Cold War when the Luftwaffe inherited some from the East German air force and tried them out in exercises.
Thus it is that huge emphasis was placed on manoeuvring capability and dogfighting in the design of the Eurofighter. The expensive Euro-jet was initially designed, in fact, as a pure fighter with no ground attack options at all – bomber capability has had to be retrofitted subsequently at still more expense. Despite lacking various modern technologies such as Stealth and thrust-vectoring the resulting Typhoon is generally touted as being one of the best air-to-air combat planes in the world right now. Certainly it is meant to be good in close fighting: it is armed with the Advanced Short Range Air to Air Missile (ASRAAM) which as its name suggests is intended for the close WVR fight.
Perhaps the account above is simply a lie, or anyway a bit of a fighter pilot tall story. But the pilot quoted will be easily identifiable inside his community if not to the outside world, and he could expect a lot of flak for telling a lie on such a matter in public. It seems likelier that the story is the truth as he perceived it: that the RAF's new superfighter was thrashed in the very type of combat it is supposed to be best at by a 1970s-era plane, albeit much modernised.
It's always possible, as the anonymous Pakistani pilot suggests, that the problem was with the crews. It may be that RAF pilots simply don't know how to fight close-in. During the many years when they had no other fighter than the lamentable Tornado F3 (the Typhoon only reached front line service a few years ago) they may have lost the institutional skillset required for dogfighting with short-range missiles.
But in general when the British forces perform badly it isn't because of a lack of skills and training. It's far more normal for them to be let down by their kit. Based on this account, the Typhoon is actually worse than an F-16, and as a result an export Flanker or Fulcrum equipped with Archer missiles would beat it easily in WVR combat.
It would appear that the Eurofighter's last remaining selling point compared to modern US-made stealth fighters which cost the same or less (or for that matter vastly cheaper ordinary non-stealth fighters like the F-16, F-18 Hornet etc) now has something of a question mark over it.
The Eurofighter hits just keep on coming. ®