Despite the increasing burden of antibiotic resistance, current approaches to eradicate pathobionts such as Staphylococcus aureus from the nasal cavity are based on the use of antibacterial agents. An alternative approach is the artificial inoculation of commensal bacteria, i.e., probiotic treatment, which is supported by the increasing evidence for commensal-mediated inhibition of pathogens. To systematically investigate the potential and the limitations of this approach, we developed a quantitative framework simulating the dynamics of the nasal bacterial microbiome by combining mathematical microbiome modeling with longitudinal metagenomic data. By inferring the structure and the magnitude of microbial interaction parameters using metagenomic data, and then simulating the nasal microbial dynamics of patients colonized with S. aureus, we could compare the decolonization performance of probiotic and antibiotic treatments under different assumptions on patients' bacterial community composition and susceptibility profile. To further compare the robustness of these treatments, we simulated a S. aureus challenge following each treatment and quantified the recolonization probability. Our results suggest that probiotic treatment clearly outperforms antibiotics in terms of decolonization performance, recolonization robustness, and leads to less collateral reduction of the microbiome diversity. Moreover, we find that recolonization robustness is highest in those patients that were not initially colonized by Dolosigranulum pigrum. Thus, probiotic treatment may provide a promising alternative to combat antibiotic resistance, with the additional advantage of personalized treatment options via using the patient's own metagenomic data to tailor the intervention. The in silico framework developed in this work is an important step forward to further investigate this alternative in clinical trials.