The lady and the tiger are alike in that each is a living creature who represents poetic justice. They are alike in that their presence will have an impact that decisively changes the life of the accused. In both cases, too, the accused will have physical contact with whichever one he chooses. Both are crowd pleasers, guaranteeing the audience a spectacle, be it an execution or a wedding.

The lady and the tiger are different in that one represents good and the other evil. Choosing the door with the lady behind it leads to an unequivocally positive outcome. The accused person is declared innocent of wrongdoing and led forth to marry the lady amid a celebratory crowd. On the other hand, choosing the tiger leads to the negative outcome of being declared guilty, killed, and eaten.

Similarities:

The lady and the tiger both share the similarity of being an unexpected outcome awaiting the alleged criminal on trial in the king's arena.  Both outcomes also occur immediately upon opening the door--the man on trial is either instantly killed or married.  Both the lady and the tiger represent extremes, of sorts, offering a dire consequence in the fashion of reward or retribution.

Differences:

The differences are naturally more easy to discern than the similarities.  The lady represents a positive reward, and the tiger, a horrible punishment resulting in death.   The possible outcomes behind the two doors could not be farther from each other.  The lady is all smiles, fairness, and grace, while the tiger is the cruelest, most vicious beast that could be procured.