The type VI secretion system (T6SS) is used by gram-negative bacteria to translocate effectors that can antagonize other bacterial cells. Models predict the variation in collections of effector and cognate immunity genes determine competitiveness and can affect the dynamics of populations and communities of bacteria. However, the outcomes of competition cannot be entirely explained by compatibility of effector-immunity (EI) pairs. Here, we characterized the diversity of T6SS loci of plant-pathogenic Agrobacterium tumefaciens and showed that factors other than EI pairs can impact interbacterial competition. All examined strains encode T6SS active in secretion and antagonism against Escherichia coli. The spectra of EI pairs as well as compositions of gene neighborhoods are diverse. Almost 30 in-planta competitions were tested between different genotypes of A. tumefaciens. Fifteen competitions between members of different species-level groups resulted in T6SS-dependent suppression in in-planta growth of prey genotypes. In contrast, ten competitions between members within species-level groups resulted in no significant effect on the growth of prey genotypes. One strain was an exceptional case and, despite encoding a functional T6SS and toxic effector protein, could not compromise the growth of the four tested prey genotypes. The data suggest T6SS-associated EI pairs can influence the competitiveness of strains of A. tumefaciens, but genetic features have a significant role on the efficacy of interbacterial antagonism.