I think we are overlooking the fact that both the MiG-15 and F-86 engines were of British design and influence, not German. The Russians got a lot of mileage out of the Rolls Royce Nene. Yes, the Allies took advantage of German technology; why not? To the Victor, the Spoils. There's no doubt that had the Germans won - as extremely unlikely as that ever was - they would have also taken advantage of Allied technology. Despite their advances they never built a successful high altitude long range heavy bomber, for example - the B-29 was far in advance of any bomber the Germans had in terms of performance, range, warload, altitude all in the same airframe. Certainly the Russians took full advantage of the type. Every subsequent Tupolev design inherited genetics researched from the B-29; it was a huge influence on post-war Soviet technology, far greater than we are led to believe in the West.
Regarding German advances - I think we tend to over emphasise their importance and subsequent impact with the benefit of hindsight. At the outbreak of WW2 Germany was no more advanced than any other country. The British also had jet engines and the He 178 airframe utilised contemporary technology, the Brits could have built one with ease. Circumstance was responsible for the Germans flying jets before the British, not advanced technology. As for rockets - Goddard built successful liquid fuelled rockets before Dornberger and von Braun. As for later in the war, we always tend to over emphasise the technology itself, rather than the environment in which it was born. many of these advanced projects came about because of the need for a 'wonder weapon' as a result of Germany's failure to secure victory conventionally. Many of them came about because the Germans were losing.
Lets look at the advances the Me 262 offered - yes, we recognise the swept wings and axial flow engines today, but at the time British gas turbines were far more reliable, easier to maintain and build - they were like the rotary radial of WW1 (although they were not reliable) - useful at that particular time even though there was more advanced stuff out there. Its worth remembering Britain also had axial flow engines during the war. Also, notice how neither the British nor the Americans scambled to put a jet into service to counter the Me 262 over Germany - jet vs jet combat had to wait until Korea (V 1s notwithstanding). Before anyone mentions the defficient range of early jets, the British were toying with in-flight refuelling before the war - a variant of the Meteor was later equipped for it.
This is in contrast to the appearance of the Fw 190, which spurred the British to create a whole new mark of Spitfire that had not been planned for. As much as the German stuff gave the Allies a nasty surprise, the threat this new technology offered was containable - piston engined fighters could and did combat the 262s and defeated them, not to mention Allied air superiority over Europe and all that entailed. As for the Me 163, too little, too late. While nothing could stop V 2s once they had been launched - the answer to the threat was bomb the crap out of launch sites and production facilities - again, Allied air superiority combined with troops on the ground approaching the Reich from East and West contained the threat.
Whilst we can marvel at their use of the technology available to them, there is no doubt that for every measure the Germans took, the Allies would have created a countermeasure. That's how the war was raged and that's how it would have continued, had it done so. Luft 46? What about RAF 46, USAAF 46 and Soviet 46? Whilst the Germans might field a host of jet fighters and bomber designs, the Allies had the capacity to out build the German designs by vast amounts, even if they might not have been as exotic. Lenin once said that "quantity has a quality all of its own". The basis of the English Electric Canberra, the A.1 bomber as proposed by Teddy Petter was put to Westland, for whom he was working during the war. Wartime pressures and production would have seen Allied jets in service pretty darn quickly - and in greater numbers than what the Germans could produce.
