Using recent values of alpha_s, the gluon condensates <alpha_s G^2> and <g^3 f_abcG^3> and the new data on the psi/Upsilon-families, we update our determinations of the MS-bar running quark masses m_c,b(m_c,b) from the SVZ-Moments M_n(Q^2) and their ratios by including higher order perturbative (PT) corrections, non-perturbative (NPT) terms up to dimension d=8 and using the degree n-stability criteria of the (ratios of) moments. Optimal results from different (ratios of) moments converge to the accurate mean values: m_c(m_c)=1264(6) MeV} and m_b(m_b)=4188(8) MeV in Table 4, which improve and confirm our previous findings [1,2] and the recent ones from Laplace sum rules [3]. Comments on some other determinations of m_c(m_c) and <alpha_s G^2> from the SVZ-(ratios of) moments in the vector channel are given in Section 5.
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