Both in class and personality, Theseus and Bottom are polar opposities.
First of all, Bottom is a manual laborer. He speaks in verse and spends his days working with his hands, while Theseus is a Duke who does very little manual work. He does the thinking and the ruling while his servants do the work.
Personality-wise, Bottom is arrogant, emotional and has a big ego. He fights for the limelight on stage and wants the attention strictly to feed his own selfish ambitions. Theseus, on the other hand, is confident but not cocky. He has center stage, but not by fighting for it. He has it because he is a wise ruler who looks out for the people.
Finally, the two charaters have very different love lives. Bottom achieves love throught the magic of Oberon. Theseus grabs his love by kidnapping the queen of the Amazons after a battle in a foreign land.