There is a lot of anecdotal and incomplete information on how military combat actually works. It is not entirely helpful that some of the worst espousers of myths are the militarise themselves. It is also not helpful that a lot of the information is buried away in very expensive, or restricted circulation volumes: sources which are often ignored by the military themselves.
Likely based on the heavy city fighting that occurred in World War 2, their is a general "truism" that the defender has an advantage in urban areas. That the attacker will have disproportionate casualties when trying to take these types of objectives.
Hakan Yazilitas, Naval Post Graduate School, June 2004
It is concluded that the attacker’s daily casualty rate is, on average, lower in urban operations.
The defenders disadvantage extends not only to urban areas, but to "close country" in general.
David Rowland, "The Effect of Combat Degradation on the Urban Battlefield" Journal of Operational Research Society, 42.7 1991, pp. 543-553 via Defense and Freedom
"Furthermore, in 1987 OA demonstrated that the defender is at a systematic disadvantage in close country (be it woods or built-up areas). It seems that, amongst other things, in close country the defender is generally unable to mass the fire of his weapons, due to very short ranges available in relation to unit frontages. Given their relative protection, if only from view, the attackers can mass forces more safely than is normal. They can therefore isolate and attack small bodies of enemy relatively easily. The overall effect was described as 'counterintuitive'. (...) Attacking infantry generally have an advantage of 3.57:1 in terms of attackers' to defender's casualties in FIBUA. (...)
Note that David Rowland, is a British officer with 25 years experience including the Falklands, and Northern Irland. So when he is doing his number crunching, he is not doing so in a vacuum.
Close country allows you to hide. It does not particularly allow you to fight more effectively. If you look at a close reading of Rommel's actions at Caporetto in the Italian-Austrian mountains during World War 1, you can see that he is using the broken up terrain to screen his advances, allowing him to either get very close to the defensive positions of the defending Italians, or to come at them from an unexpected direction. But to see what is happening, you have to look at a more detailed account of what is going on than his very brief descriptions in his memoirs.
A lot of the complaints about the terrain that the Western Allies fought over in World War 2 is likely more of a problem with superior German training, doctrine, and motivation. The broken terrain likely helped the German's hide from the Allies superior air power, but did not directly cause them to inflict disproportionate casualties. Records indicate that the Western Front had heavier day-to-day casualties relative to the troops deployed (more firepower in a smaller area) but do not indicate that the Germans anything more than their usual advantages.
To bring this back down to the low level skirmishing affairs we are often discussing, the net effect of rough terrain is to slow up movement, and make initial concealment easier. But in a pitched battle, where the defenders have chosen to stand their ground, it also means that an aggressive opponent cannot be stopped from getting in close. And as we have discussed before, the closer the combatants are, the deadlier the fighting gets.