The structuralist paradigm to discourse analysis defines discourse as "language above the sentence" and is based on the premise that language is a mental phenomenon (thus you'll see shades of Chomsky).  The functionalist paradigm focuses on language use and is based on the premise that language is a social phenomenon.
 
 
 

Structuralist	Functionalist
"etic"--analysis based on form	"emic"--analysis based on meaning
Code-centered	Use-centered
Analyze code first	Analyze use first
Referential function	Social function
Elements/structures are arbitrary and universal	Elements/structures are ethnographically appropriate
All languages equivalent	Languages and varieties not necessarily equivalent
One code	Code diversity
Fundamental concepts taken for granted	Fundamental concepts problematic and to be investigated

Adapted from Deborah Shiffrin, Approaches to Discourse, 1994.