We report extended simulation results and their new analysis in two important gauge theories with twelve fermion flavors in the fundamental SU(3) color representation and two fermions in the sextet representation. We probe the $N_f=12$ model with respect to the conformal window using mass deformed finite size scaling (FSS) theory driven by the fermion mass anomalous dimension. Our results at fixed gauge coupling show problems with the conformal scenario of the $N_f=12$ model. In the sextet model with two flavors, under the conformal hypothesis, we determine large values for the anomalous fermion mass dimension with $\gamma\geq 1$. Since our sextet analysis favors the chiral symmetry breaking hypothesis without conformality, the large exponent $\gamma$ could play an important role in understanding the composite Higgs mechanism. The new results discussed here include our extended data sets and exceed what was presented at the conference. Comment: Contribution to the XXIX International Symposium on Lattice Field Theory - Lattice 2011