Well not really. The 40mm and 37mm rounds can only compare due to the diameter of the projectile, but not much past that.

The 40mm round (MkIIT) contained about 59 grams of explosive
The 37mm Round (M63) contained 39 grams of explosive

The 40mm round had a muzzle velocity of 868 meters per second
The 37mm round had a muzzle velocity of 785 meters per second

The 40mm projectile weighed 907 grams
The 37mm projectile weighed 331 grams

The 40mm had an armour penetration of about 25mm
The 37mm had an armour penetration of about 25mm (the M63 was not the optimum AP 37mm round) 37mm AP rounds were solid rounds with no explosive.

Any numbers about armour penetration is HIGHLY dependent on armour type, range, and angle of impact so they can only be used as a VERY approximate figure.

Sources

http://en.wikipedia.org/wiki/37_mm_Gun_M3#Ammunition
http://www.wwiiequipment.com/index.p...raft&Itemid=58

Carlas Hathcock.
 

Gunnery Sargent Carlos Hathcock used a scope mounter .5 browing M2 in Vietnam, Peoples Republic of, to devesating effect. I believe that the 40mm and 20mm were used to supress enemy deck gun crews while the 4 inch dealt the damage. Good hunting.

Fair enough. But I only meant "roughly". It should be added that since the 40mm was intended as an anti-air gun, it's HE shells cannot compare to tank HE shells, and even less compare to tank AP shells. There are othee issues too, such as the projectile/propelant ratio, which makes all the difference since it is purpose-related. Tank ammo (AP) was intended to have an as high as possible muzzle velocity, for penetration reasons, which is not the case with the 40mm either.