If we are comparing Cavill's Superman with Chris Evan's Captain America, then we have seen only 2 movie with Superman, so to be fair, we need to see only first two movies of Captain America, namely Captain America : The First Avenger and Avengers.
Looking at Captain America's trilogy and two ensemble movies gives him unfair advantage, don't you think ?
Also, I agree with what Miss Lane said, Cavill's Superman is constantly compared with old portrayal of Superman, which proves to be troublesome when a new director wants to have some degree of artistic freedom to show his version of the character.
Captain America does not face such problem, in addition, people have preconceived notions of how Superman should behave, Superman cannot kill, which Captain can, as he is considered to be a Soldier.
We have seen that Captain cripples / kills / shoots many people, fans still consider him to be a wholesome "Boy Scout", Superman does not get such free pass.
Edit: And, there's the alien angle, which Superman has, people don't trust him as he is Kryptonian, Captain America faces no such problem, in addition as Superman possesses super-powers, many people (in DC universe) consider him as a threat, again no such problem for Captain America, so it is relatively easy for Captain America to get the label of "Boy Scout", which is why it's easier for writers to write story for his character, and they (Marvel) have done a good job of it, still, it was not as difficult to write a story for him.