The branching ratios of the different reaction pathways and the overall rate coefficients of the dissociative recombination reactions of CH3OH2+ and CD3OD2+ have been measured at the CRYRING storage ring located in Stockholm, Sweden. Analysis of the data yielded the result that formation of methanol or deuterated methanol accounted for only 3 and 6% of the total rate in CH3OH2+ and CD3OD2+, respectively. Dissociative recombination of both isotopomeres mainly involves fragmentation of the C-O bond, the major process being the three-body break-up forming CH3, OH and H (CD3, OD and D). The overall cross sections are best fitted by sigma = 1.2 +/- 0.1 x 10(-15) E(-1.15 +/- 0.02) cm2 and sigma = 9.6 +/- 0.9 x 10(-16) E(-1.20 +/- 0.02) cm2 for CH3OH2+ and CD3OD2+, respectively. From these values thermal reaction rate coefficients of k(T) = 8.9 +/- 0.9 x 10(-7) (T/300)(-0.59 +/- 0.02) cm3 s(-1) (CH3OH2+) and k(T) = 9.1 +/- 0.9 x 10(-7) (T/300)(-0.63 +/- 0.02) cm3 s(-1) (CD3OD2+) can be calculated. A non-negligible formation of interstellar methanol by the previously proposed mechanism via radiative association of CH3+ and H2O and subsequent dissociative recombination of the resulting CH3OH2+ ion to yield methanol and hydrogen atoms is therefore very unlikely.