(Abridged) Most massive stars are located in multiple systems. The modeling of disk fragmentation, a possible mechanism leading to stellar multiplicity, relies on parallel 3D simulation codes whose agreement remains to be evaluated. Using the Cartesian AMR code RAMSES, we compare disk fragmentation in a centrally-condensed protostellar system to the study of Oliva & Kuiper (2020) performed on a grid in spherical coordinates using PLUTO. Two RAMSES runs are considered and give qualitatively distinct pictures. When allowing for unlimited sink particle creation, gas fragmentation leads to a multiple stellar system whose multiplicity is affected by the grid when triggering fragmentation and by numerically-assisted mergers. On the other hand, using a unique, central, fixed sink particle, a centrally-condensed system forms, similar to that reported in PLUTO. The RAMSES-PLUTO comparison is performed with the latter: agreement between the two codes is found regarding the first rotationally-supported disk formation, the presence of an accretion shock onto it, the first fragmentation phase. Gaseous fragments form and their properties are in agreement between the two codes. As a minor difference, fragments dynamics causes the disk structure to be sub-Keplerian in RAMSES whereas it is found to be Keplerian and reaches quiescence in PLUTO. We attribute this discrepancy to the central star being twice less massive in RAMSES because of the different stellar accretion subgrid models. In a centrally-condensed system, the agreement between RAMSES and PLUTO regarding many of the collapse properties and fragmentation process is good. Fragmentation occurring in the innermost region and numerical choices (use of sink particles, grid) have a crucial impact when similar but smooth initial conditions are employed - more crucial than the code's choice - on the system's outcome, multiple or centrally-condensed.