The formula that I have seen for Momentum is:
Mass x velocity / {weight(7000gr =1 lbs) x gravity(32.174)} = 225218. Measured in Slug-feet.
Right. Well, nearly right. The formula should be stated as:
Weight{grains} x velocity{fps} / (7000 x 32.174...)
We don't measure mass in the english system, we measure weight. The denominator is a couple of conversion factors required to get the units right when dealing with the english measurement system. You have to convert from from grains to lbs (divide by 7000) and then from lbs to slugs (divide by 32.1740486... . Slugs are the english system's unit of mass.
After all the conversions you have Momentum = mass{slugs} x velocity{fps}
If you do it in kilograms and meters per second you can dispense with the need for conversions since kilograms are already a measure of mass.
If we determined handgun effectiveness using momentum, then the 45 acp (in that example) is clearly better (17%); however, according to KE the .357 Sig is "more powerful".
It's a mistake to look at either momentum or KE as a direct measure of handgun effectiveness. Neither one tells the whole story by itself, and even the two of them together still leave a lot to be desired.
In my opinion, it is not possible to find a formula that provides a single number measure of handgun effectiveness.
Momentum and energy both provide some insights into the potential of a projectile to damage/apply force to/penetrate a target medium, but there are many, many reasons a projectile might not live up to its potential and many, many reasons why even if it does, the target may not be rapidly incapacitated.
Like I said, KE is highly velocity dependent.
It is what it is. KE is the measure of the potential of a projectile to do work (cause damage, if you will). It can be used, in combination with penetration to determine the amount of force applied to a target medium by a projectile that stops in the target medium.
It's not something that someone made up because they liked velocity, it's a scientific quantity, measuring an important parameter of a moving object, verifiable via repeatable experiments.
It doesn't tell the whole story of projectile effectiveness--not by a long shot--but the idea that it should be dismissed or discounted because the results it provides don't match popular theories of bullet effectiveness or personal opinions is extremly problematic from a scientific standpoint.
The problem isn't that it is highly velocity dependent or that it doesn't provide intuitive results, the problem is that people try to make it mean more than it really does.