In Ben Johnson's The Alchemist, a trusted servant takes advantage of the master of the house in order to dupe citizens for the purpose of attaining illegitimate monetary gain. In Shakespeare's Macbeth, a trusted nobleman and aristocrat takes advantage of the trust and generosity of his king in order to illegitimately gain power over him--even unto his death--and the entire kingdom and thus usurp the throne for his own selfish advancement--spurred on, of course, by the greedy and overly ambitious Lady Macbeth. Thus there are comparisons in the overall plot of each, yet there are contrasts in the quality and degree and outcomes of the deceptions and evils perpetrated.
Both pieces of writing do deal with characters who pursue their goals. I'm not quite sure if I can make my train of thought clear, but it seems to me that in The Alchemist he went in search of something that ended up being right where he started. However, if it were not for his journeys, would he have ever recognized this? Macbeth on the other hand chose to take the shortcut in order to achieve his goals. Had he taken the same sort of journey, would his life have turned out the same?
I think the obvious thing to go for is the way that both characters pursue a goal or a dream. Clearly this is the major similarity in both of these texts, however, what you will want to focus on is the motive and the method of how both protagonists pursue their goals. This of course leads to the different tone and message of each text.
These are two of my favorite pieces of literature. Shakespeare's Macbeth tells the story of a man who has a dream, but his choices to realize that dream begin with murder and continue that way until he is defeated at the end. In Paulo Coelho’s The Alchemist, Santiago is also pursuing his dream, however, he is patient on his journey and succeeds.
In both stories, there is someone important to offer advice. In Macbeth, it is Lady Macbeth, but her advice is self-serving and deadly. In The Alchemist, Santiago has several people who help him along the way, but perhaps the most important is the old man, Melchizedek (the King of Salem) whose advice is steeped in finding one's treasure by having faith and following a "righteous" path.
The stories are very different also in that Macbeth is a dark tragedy, while the mood and tone of The Alchemist is bright and hopeful, even in the face of life's disheartening obstacles.
If I had to write an essay comparing these two pieces of literature, I think I would concentrate on the different method each main character uses in order to achieve his dream, and the ultimate result of following that method.