Immunocompromised patients have been shown to have an impaired immune response to COVID-19 vaccines. Here we compared the B-cell, T-cell and neutralizing antibody response to WT and Omicron BA.2 SARS-CoV-2 virus after the fourth dose of mRNA COVID-19 vaccines in patients with hematological malignancies (HM, n=71), solid tumors (ST, n=39) and immune-rheumatological (ID, n=25) diseases. We show that the T-cell response is similarly boosted by the fourth dose across the different subgroups, while the antibody response is improved only in patients not receiving B-cell targeted therapies, independent on the pathology. However, 9% of patients with anti-RBD antibodies did not have neutralizing antibodies to both virus variants, while an additional 5.7% did not have neutralizing antibodies to Omicron BA.2, making these patients particularly vulnerable to SARS-CoV-2 infection. The increment of neutralizing antibodies was very similar towards Omicron BA.2 and WT virus after the third or fourth dose of vaccine, suggesting that there is no preferential skewing towards either virus variant with the booster dose. The only limited step is the amount of antibodies that are elicited after vaccination, thus increasing the probability of developing neutralizing antibodies to both variants of virus. Hence, additional booster doses are recommended to frail patients.