In a nutshell: NS-37 is the superior gun, the BK 3,7 uses the superior ammo.
The NS-37 has the advantage of higher ROF, higher muzzle energy and much more ammo. The German Hartkern shell is much lighter and faster, should have a significantly higher penetration ability at optimum angles (but is quite sensitive to angle changes).
Unfortunately, unlike tank guns we don't get penetration data for airborne AT guns in AH. Anthony G. Wiliams gives a penetration of 48mm at 500m/90° for the NS-37, according to official German test data the BK 3,7 with Hartkern will penetrate 95mm at 600m/90° (at 100m that can go up to 140(!)mm)
In game the 40mm Vickers has in my experience about the same or slightly better penetration than the NS-37.