My professor was against the idea more on principle. He did not think it was useful, or historically valid, to make diachronic comparisons like that. I can't do justice to his reasoning, because I don't really understand it, and I do not share his beliefs. I do think comparisons of historical phenomena across time can be useful, and I see no reason why military effectiveness should not be included.
Therefore, I was interested to discover the television series "Deadliest Warrior," which compares weaponry of various famous armies, from modern times (Navy SEALS, the FBI) to ancient history (the Persian Empire, Sparta). They choose four weapons from each army -- long range, medium range, short range, and special -- and compare how much damage they can do. They then run a computer simulation using their results to determine which side wins the majority out of 1000 combats, and declare the winner "the deadliest warrior." They have, as far as I can tell, not made the mistake of pitting soldiers with modern firearms against those who have to fight with swords and spears. Nevertheless, the series is silly in many ways.
The focus on weapons is understandable, as it is concrete and easier to quantify, but it still pretty much undermines any attempt to reach an overall conclusion. First, they act as though every soldier carried all four weapons -- that's the only way the simulation can work -- which is very rarely the case historically. Second, they evaluate the weapons in terms of one-on-one combat. While there are some weapons for which this makes sense, there are others that it makes a mockery of.
As an extreme example, consider the pike, essentially a long spear. One person with a pike is hardly a dangerous competitor. His weapon is maybe 10, maybe 14 feet long, and the only dangerous part is the very tip. Even if it wasn't very heavy -- which it was -- it still would have been virtually impossible to maneuver against a single opponent because of its length. (If you want an idea of how difficult, take a laser pointer and aim it at a wall 14 feet away. You will find that the light on the wall moves around as if you suffered from palsy, because every little move your hand makes gets magnified over the distance to the wall.) You could easily get around the point of the pike, at which time he would be at the mercy of whatever shorter weapon you possessed. Put a block of several hundred men with pikes together, however, and the situation is reversed. Then your sword, no matter how large, will seem puny as a wall of pike points advances toward you. If you get pase the first rank, you will face another rank of pikes, and another, and another. Unless the pike square gets disorganized, it is virtually unbeatable by non-projectile weapons.
I haven't seen any pikemen on Deadlist Warrior -- no doubt for good reason -- but every comparison of weapons must suffer to some extent from the failure to consider how the weapons were employed tactically. To pick an example, they recently analyzed a Comanche scalping knife against some kind of Mongolian bladed weapon. It was totally pointless, as the scalping knife was never intended as a battle weapon, as they fully admit on the show. It was apparently used to kill (not just to scalp), but it was a very small weapon used chiefly in raids and ambushes, not something to be wielded against a mass enemy. They were debating whether the Comanche would be able to get in close against the Mongolian warrior, as though they would ever be facing each other armed just with those weapons.
Another dubious point is that they test the timing and accuracy of the weapons by having a modern Comanche descendant and Mongol use them. While I am impressed with the skill these people showed with the bow while mounted, it cannot possibly compare to the ability of the actual warriors (on either side), who learned how to ride and shoot at an early age and, at least for the Mongols, spent virtually their whole lives practicing.
Having said those negative things (in brief: don't believe any of the conclusions of the show, they are meaningless), I am still impressed with Deadliest Warrior in several ways. First, they have assembled some experts capable of creating and evaluating some very interesting tests on these weapons. I know something about modern attempts to test 17th and 18th century firearms, and it is very difficult to do. It is great that they are able to do this; their experiments will become historical evidence, even if their conclusions are ignored. I am interested in how they managed to recreate these weapons. They might be using historical artefacts in some cases, but we certainly don't have any Mongolian bows from the 13th century left around. Of course, this also opens up the possibility that the recreations are not entirely authentic. Creating a Mongolian compound bow, which consists of layers of bone, sinew, and wood, was a complicated art, and I'm sceptical how easily we can do that today.
Second, I am surprised and interested to see ethnic relatives of the warriors who know so much about combat. Some people take this stuff very seriously, and they obviously care about the outcome on more than a scientific level. It's one thing to know about weapons, but quite another to be able to use them effectively.
Third, I have to say that this show is a great idea for attracting interest in history. I'm always alert to ways to make history appealing to people, and this is certainly a striking one. It is a little disturbing to see conclusions being drawn from just weaponry, but at least they are doing really interesting experiments with weapons, and I'm sure many people will be drawn to learn more about some of these armies through the show.