The local Langlands conjectures imply that to every generic supercuspidal
irreducible representation of $G_2$ over a $p$-adic field, one can associate a
generic supercuspidal irreducible representation of either $PGSp_6$ or$PGL_3$.
We prove this conjectural dichotomy, demonstrating a precise correspondence
between certain representations of $G_2$ and other representations of $PGSp_6$
and $PGL_3$ when $p \neq 2$. This correspondence arises from theta
correspondences in $E_6$ and $E_7$, analysis of Shalika functionals, and spin
L-functions.