However by reading the comments and comparing the votes I still think that most people want to go with the politically correct answer.
From my perspective: Rome wealthy, organized and technologically advanced managed to subdue the regions of Spain, France, England, Egypt, Greece, Syria, etc. Brutal power which was funded by wealth not by understanding any culture, military strategy was important but at the core is to FUND the army.
England, same case with its navy.
Spain, a bit different - Strategy to take over the Aztec and their gold allowed for massive land conquest.
Mongols: no cash whatsoever, nor cultural understanding.
In general, I don't see how understanding the culture of the enemy matters at all in army vs army warfare.
Yes, guerrilla warfare is a different thing, its a modern phenomenon which rises from a personal belief, not because the fighters are getting paid to kill the enemy as is the case in traditional armies. Historically, FUNDING the war is the ultimate factor, fund science come up with a bigger gun, give it to your army, or the Persian way - Hire mercenaries pay them up and continue on.
Anyone voting for "Understanding the culture and the people of the enemy" please write a coherent argument, validating such response.
A few days after the poll, and 4:1 votes, still no one has clearly explained why this is important. Again, it may be the politically correct answer, but if you can't defend it I cannot accept it.