We compare two natural bases for the invariant space of a tensor product of
irreducible representations of A_2, or sl(3). One basis is the web basis, defined from a
skein theory called the combinatorial A_2 spider. The other basis is the dual canonical
basis, the dual of the basis defined by Lusztig and Kashiwara. For sl(2) or A_1, the web
bases have been discovered many times and were recently shown to be dual canonical by
Frenkel and Khovanov. We prove that for sl(3), the two bases eventually diverge even though
they agree in many small cases. The first disagreement comes in the invariant space
Inv((V^+ tensor V^+ tensor V^- tensor V^-)^{tensor 3}), where V^+ and V^- are the two
3-dimensional representations of sl(3). If the tensor factors are listed in the indicated
order, only 511 of the 512 invariant basis vectors coincide.