I thought NATO used, for the most part, US equipment and that US equipment was vastly superior to anything the Soviets had.
Actually, it is.
1) The "short-range" missile (heat-seeking, I think) is the Sidewinder for both NATO and the US. It has a range of 10 nm, which outranges Soviet short-range missiles and guns. It can be used safely against many Soviet planes and, with some degree of risk, against the best Soviet planes.
2) The "medium-range" missile (radar guided, I think) is the Sparrow for the US (24 nm) and the Sky Flash for NATO (27 nm). It can be used safely against any real Soviet plane; the Soviet medium-range missiles have a range of 16 and 19 nm.
3) Then there's the Phoenix.
Of course, NATO is always heavily outnumbered. If the Soviets all come at once, you've got a problem. But if they come in waves so that your planes can reload their missiles, then your force is effectively larger.