Patients after organ transplantation have impaired immune response after vaccination against the SARS-CoV-2 virus. So far, published studies have reported quite different response rates to SARS-CoV-2 vaccination, ranging from 15–79% in liver and kidney transplant recipients. Up to one year after the first vaccine dose, we analyzed the humoral and cellular immune response of 21 liver transplant (LTX) patients after vaccination with mRNA vaccines compared with 28 kidney transplant (KTX) patients. We evaluated IgG against the SARS-CoV-2 spike protein as well as SARS-CoV-2 specific T cells using an ELISpot assay that detected IFN-γ- and/or IL-2-expressing T cells. We found a cellular and/or humoral immune response in 100% of the LTX patients compared with 68% of the KTX patients. Antibody titers against the spike protein of SARS-CoV-2 were significantly higher in the LTX group, and significantly more LTX patients had detectable specific IL-2-producing T cells. The immunosuppression applied in our LTX cohort was lower compared with the KTX cohort (14% triple therapy in LTX patients vs. 79% in KTX patients). One year after the first vaccination, breakthrough infections could be detected in 41% of all organ transplant patients. None of those patients suffered from a severe course of COVID-19 disease, indicating that a partial vaccination response seemed to offer protection to immunosuppressed patients. The better immune response of LTX patients after SARS-CoV-2 vaccination might be due to less intense immunosuppressive therapy compared with KTX patients.