The two T-box transcription factors T-bet and Eomesodermin (Eomes) are important regulators of cytotoxic lymphocytes (CTLs), such as activated CD8 T cells, which are essential in the fight against intracellular pathogens and tumors. Both transcription factors share a great degree of homology based on sequence analysis and as a result exert partial functional redundancy during viral infection. However, the actual degree of redundancy between T-bet and Eomes remains a matter of debate and is further confounded by their distinct spatiotemporal expression pattern in activated CD8 T cells. To directly investigate the functional overlap of these transcription factors, we generated a new mouse model in which Eomes expression is under the transcriptional control of the endogenous Tbx21 (encoding for T-bet) locus. Applying this model, we demonstrate that the induction of Eomes in lieu of T-bet cannot rescue T-bet deficiency in CD8 T cells during acute lymphocytic choriomeningitis virus (LCMV) infection. We found that the expression of Eomes instead of T-bet was not sufficient for early cell expansion or effector cell differentiation. Finally, we show that imposed expression of Eomes after acute viral infection promotes some features of exhaustion but must act in concert with other factors during chronic viral infection to establish all hallmarks of exhaustion. In summary, our results clearly underline the importance of T-bet in guiding canonical CTL development during acute viral infections.