Dissociative recombination of the polyatomic ions D3O+ and H3O+ with electrons have been studied at the heavy-ion storage ring CRYRING (Manne Siegbahn Laboratory, Stockholm University). Absolute cross sections have been determined from 0.001 eV to 0.25 eV center-of-mass energy for D3O+ and from 0.001 eV to 28 eV for H3O+. The cross sections are large (7.3x10(-13) cm(2) for D3O+ and 3.3x10(-12) cm(2) for H3O+ at 0.001 eV). At low energies, the cross sections for D3O+ are E-1 energy dependent whereas it is slightly steeper for H3O+. A similar E-1 energy dependence was also observed by Mul [J. Phys. B 16, 3099 (1983)] with a merged electron-ion beam technique for both H3O+ and D3O+ and by Vejby-Christensen [Astrophys. J. 483, 531 (1997)] with the ASTRID storage ring in Denmark, who presented relative cross sections for H3O+. A resonance has been observed around 11 eV for H3O+. It reflects an electron capture to Rydberg states converging to an excited ionic core. A similar structure was reported by Vejby-Christensen Our absolute measurements are in fairly good agreement with those from Mul , which were first divided by 2 (Mitchell, 1999, private communication) and from Heppner [Phys. Rev. A 13, 1000 (1976)] for H3O+. Thermal rates were deduced from the measured cross sections for electron temperatures ranging from 50 K to 30 000 K. At 300 K, the thermal rate is equal to 7.6x10(-7) cm(3) s(-1) for H3O+ and to 3.5x10(-7) cm(3) s(-1) for D3O+. Complete branching ratios for all the possible product channels have been determined from 0 eV to 0.005 eV center-of-mass energy for D3O+ and at 0 eV for H3O+, using a well-characterized transmission grid in front of an energy-sensitive surface-barrier detector. No isotope effect was observed within the experimental uncertainties. The three-body break-up channel OX+X+X (where X stands for H or D) is found to occur for 67%-70% of the dissociations. Water or heavy water is produced with an 18%-17% probability and the production of oxygen atoms is negligible. These results support the three-body break-up dominance already found by Vejby-Christensen for the DR of H3O+ in a similar heavy-ion storage ring experiment. However, even if the general trend is the same for both storage rings, significant differences have been observed and will be discussed.