Most generally, three different specifications are given by the manufacturer for a given cartridge loading: the weight of the bullet expressed in grains (1/7000 of a pound abbreviated as gr), the velocity of the bullet at the muzzle of the manufacturer's test barrel expressed in feet per second (abbreviated as fps) and the kinetic energy of the bullet at the muzzle of the test barrel expressed in foot-pounds (commonly abbreviated as ft lbs or fpe). Sometimes, particularly when the ammunition is produced in countries other than the United States, these specifications may be expressed in different units of measure. European ammunition often lists bullet weight in grams (g), velocity in meters per second (m/sec), and kinetic energy in joules (j). One must remember, however, that while the units of measure are different, what they are actually measuring are still the same (weight, velocity, and kinetic energy).
If we use your example of the .380 Auto and pick a given loading, say a Winchester Silvertip, we see that Winchester advertises an 85 grain bullet with a muzzle velocity of 1000 feet per second from a 3.75 inch test barrel that produces 189 foot-pounds of kinetic energy at the muzzle of the 3.75 inch test barrel.
Now, as far as what makes a given cartridge or loading "better" than another, that is a topic which continues to be hotly debated. If we compare, for example the Winchester Silvertip .45 ACP loading to the aforementioned Silvertip .380, we find that while the velocity is the same (1000 fps), it has a much heavier bullet (185 gr) and substantially more energy (411 ft lbs). Some would say that the extra energy of the .45 ACP loading makes it "better" as in more effective at incapacitating someone/something than the .380 Auto. Others would say that the extra weight (which generally yields deeper penetration) and/or the larger diameter(.451" vs. .355") of the .45 make it "better" than the .380. Still others might feel that the reduced recoil of the .380 Auto makes it easier to shoot well and thus trumps the greater mass, diameter, penetration, and energy of the .45 ACP.