The advantage on #GWAS is that you can explore the genetic determinism of traits which are not polymorphic inside a population. Also it is not affected by #LinkedSelection and you can detect the precise sites which have shifted in directional selection.

Two shortcomings : 1) You can only study #homoplasy (i.e convergent traits). 2) You can only detect sites associated to a trait in protein coding genes (for now). (2/N).