With the exception of the atomic bomb, it's hard to think of a technological innovation developed during wartime, diverting resources from traditional combat tech, that changed the outcome of the war significantly.
What one has to remember, though, is that Germany was significantly more resource constrained than the Allied powers. Resources are not always fungible. If you have a shortage of steel and manpower, and a relative glut of engineering talent, it behooves you to invest heavily in R&D to use that steel as efficiently as possible and equip those men as well as possible.
In some ways, Germany was doomed the day America entered the war to be ground between the gears of superior industrial powers. They had to claw for some doctrinal or technological advantage, however remote the possibility, because the outcome of trading losses at a 1:1 ratio was absolutely obvious.
The Nazis were a huge fan of the technological approach - they even called them "Wonder-weapons". In actual fact the vast majority of the "Wunderwaffe" were duds for one reason or another - a major cause was rushed development due to the desire to have the technology now.
No discussion of the two philosophies is complete without mentioning A.C. Clarke's 1951 short science fiction story "Superiority", which was doubtless influenced by the Nazi failure.
https://en.wikipedia.org/wiki/Wunderwaffe http://www.mayofamily.com/RLM/txt_Clarke_Superiority.html