The answer to this question could be as simple as grabbing a famous director -- Steven Speilberg -- and two of his better-known films -- Schindler's List and Lincoln. However, the comparison creates a better essay if there is an underlying theme to be examined, not just pushing two movies together to see what's similar.
For example, if you chose the works of Hong Kong director John Woo, you would find that many of his films involve a concept called "Heroic Bloodshed." Among other concepts, the heroes are called on to be as brutal as the villains, because otherwise, they are sure to lose; the bloodshed is therefore justified as necessary to rid the world of evil and save more innocent lives. Two films by Woo are A Better Tomorrow and Hard-Boiled.
Another example is American director Terrence Malick. Malick has only directed six films, but he is considered one of the all-time greats. Malick's early films focused on the role of Man in nature, and how frequently Man is violent and self-absorbed. Two films by Malick are Badlands and Days of Heaven.
Alfred Hitchcock is often considered one of the best directors in history. His works are thematically complex, covering a wide range of human emotion and interaction, but most of his films share a theme of ordinary people caught up in extraodinary circumstances. Two films by Hitchcock are The 39 Steps and Strangers on a Train.
Regardless of which director and films you choose, you should focus on only one or two themes to follow; trying to list all the possible themes of two separate movies, even by the same director, would be unnecessarily complex. Instead, take overall themes or the strongest theme from both films, and compare them to see how the director has changed style or attitudes. This will give insight both into the films themselves and into the broader work of the director.