I see that those two compounds mean husband and wife, as a married couple. But is there a difference in usage or context?
They mean the same thing but 夫妻【fusai】is more polite.
For example, you can use 夫婦【fuufu】to refer to yourselves (私たち夫婦), you can use for others and use it formally (ご夫婦). But you can't use 夫妻【fusai】to refer to yourselves (私たち夫妻 = NG).
Also when speaking formally, ご夫妻 is better than ご夫婦.
夫妻 is the more formal of the two, and shouldn't be used when talking about yourself or people from your inner circle. As a general rule of thumb, use 夫婦 for such close relations or for general comments about married couples, and 夫妻 when talking about people outside your group.
As the other two answers say,
夫妻 'husband and wife' is a more proper way to say. That is probably because
夫婦 'huband and woman' is not politically correct. Interestingly, it goes the opposite of the phrase used in Western wedding ceremony: 'man and wife', but the idea is the same; both phrases are based on sexual discrimination.
However, since the word
夫婦 is more established, it appears in many compound nouns, where it cannot be replaced with
夫妻, even in legal terms:
夫婦漫才 (but not 夫妻漫才)
夫唱婦随 (but not 夫唱妻随)
夫婦喧嘩 (but not 夫妻喧嘩)
夫婦財産制 (but not 夫妻財産制)
夫婦別姓 (but not 夫妻別姓)
夫妻 cannot be used alone as a word. It needs to be used as a part of a word. I.e.,