In The Merchant's Tale, Januarie wants to get married basically for the only reason of lawful sex and to produce an heir. He marries May, who is not even 20 yet, mostly due to lust for her. It is not told why she marries him, perhaps for a better social standing, since Januarie is very wealthy. Damyan sees and falls in love with May. Damyan and May end up having an affair, and Januarie loses his sight. He gets it returned to him to see May and Damyan together. May convinces him that he didn't see what he thought he saw. The story ends with May and Januarie staying married, but it is implied that she will continue to be unfaithful with Damyan.
In The Knight's Tale, Arcite and Palamon are cousins, who are arrested and put in prison by the Duke of Athens. Palamon looks out of the window in the tower where they are being held. The tower overlooks a beautiful garden. He sees Emily there and falls in love with her. Arcite awakes and sees her as well, and also falls in love with her. This begins a competition between the two cousins and they grow to hate each other. Arcite gets released and disguises himself so he can work in Emily's house. Palamon escapes from prison. The two are going to be in a duel and the winner gets to marry Emily. Palamon prays to Venus to marry Emily. Arcite prays to Mars for victory and Emily prays to Diana to stay unmarried. She also asks that if she has to marry that she marry the one who truly loves her. The story ends with Arcite winning the battle. Palamon is wounded by a sword, but Arcite is thrown from his horse. Arcite wins, but dies and tells Emily before he dies to marry Palamon. In the end all of the prays are answered.
As you can see the two stories are similar, in the way that there is one woman and two men who want her. In The Merchant's Tale, May is wanted for selfish reasons. Januarie only wants her because she will allow him to have what he wants. May marries him probably for wealth. Damyan may love her, but the two are unfaithful. This story is about three people who will do whatever it takes to get what they want. However in The Knight's Tale you can see that there is real love here. Both Artice and Palamon fall in love with Emily. Even though the two men become competitors for Emily, by the end of the story you can see that Artice still loves his cousin. He tells Emily to marry Palamon, because he knows that Palamon truly loves Emily. The Knight's Tale is a real love story, while The Merchant's Tale is a love story with a tragic outcome for all three involved.