Connes mentions Barrett's paper in his paper. He appears to have ironed out a few flaws in the SM picture, but does not claim to explain things such as the number of generations (which we all know comes from orbifold Euler characteristics) or precise particle masses.
Barrett similarly acknowledges the independence of Connes' work in his paper. Both papers claim to have reached some understanding of neutrino mass generation, based on Connes' SM. They conclude that one must consider an internal space of signature 6 (mod 8) rather than 0.
Connes considers hopeful possibilities in the conclusion: ... or even that the fundamental theory has selected a preferred scale and is a fully unified theory at the operator theoretic level (ie. a kind of spectral random matrix theory where the operator D varies in the symplectic ensemble).