Context. The coagulation of dust particles is the initial step in planetary formation, with the precursors to planetesimals believed to form via the collisions of micron and submicron sized dust particles in the disk surrounding a newly formed protostar. One of the usual assumptions in numerical models of aggregation is that of spherical monomers. However, the polarization of light in the interstellar medium (ISM) indicates that dust particles may not necessarily be spherical. Aims. This study investigates the influence of monomer shape (ellipsoidal vs. spherical) on the morphology of aggregates. The ellipsoidal grains used are prolate with an axis ratio of 3:1:1, which current evidence suggests as a possible shape for instellar dust grains. Methods. Populations of aggregates are built from ellipsoidal monomers and spherical monomers using both particle-cluster aggregation (PCA) and cluster-cluster aggregation (CCA) regimes incorporating the rotation of particles. The morphology of the resulting aggregates is compared using the maximum radius, porosity, fractal dimension, compactness factor and friction time. The last two factors indicate how the dynamics of a population of dust may be altered depending on monomer shape. Results. The results of this study indicate that monomer shape plays an important role in determining the final morphology of aggregates. Comparing ellipsoid grains with 3:1:1 axis ratio to spheres, the greatest difference is seen in compactness factors: (∼18%) for the PCA regime, reaching a maximum of (∼80%) for the CCA regime. The influence on porosity is also appreciable, (∼8%) and (∼15%) for PCA and CCA regimes respectively. The resulting differences for the friction times depend on the collision regime employed, yet show a marked difference for the different monomer shapes, (∼12%) for PCA and (>50%) for CCA at large sizes. It is concluded that the effect of monomer shape in the hit-and-stick aggregation model may produce appreciable structural variation in the final aggregate. Present models of fluffy aggregates made up of only spherical monomers therefore may not be the best representation for grains in some astrophysical environments.