When we compare something to something else, we are placing two things—sometimes very different things—in the same category and commenting on connections we perceive. We are expressing an opinion or making an observation. Others might not have noticed these similarities; still others might disagree with them. Some examples: I'd compare the view from your living room to a painting by Bierstadt. Ruben compared Giorgio's spaghetti to dog food. Note that these are subjective statements—they are not verifiable.
When we compare something with something else, we are not expressing opinions or making personal statements. We are placing two things side by side and noting empirical similarities and differences. Our purpose is to be fair and impartial. The accuracy or inaccuracy of our findings can be verified. For instance, if we compare apples with oranges, we find that neither fruit contains fat, cholesterol, or sodium; that oranges contain more than twice as much potassium as apples; that a cup of oranges contains twenty more calories than a cup of apples.
In the writer's guide Simple and Direct Jacques Barzun issues this caveat: "Any writer can compare himself with Shakespeare and discover how far he falls short; if he compares himself to Shakespeare (i.e., puts himself on the same level), then he had better think again."