(1) Background: In children, SARS-CoV-2 infection is mostly accompanied by mild COVID-19 symptoms. However, multisystem inflammatory syndrome (MIS-C) and long-term sequelae are often severe complications. Therefore, the protection of the pediatric population against SARS-CoV-2 with effective vaccines is particularly important. Here, we compare the humoral and cellular immune responses elicited in children (n = 15, aged 5–11 years) vaccinated with the RBD-based vaccines SOBERANA® 02 and SOBERANA® Plus combined in a heterologous scheme with those from children (n = 10, aged 4–11 years) who recovered from mild symptomatic COVID-19. (2) Methods: Blood samples were taken 14 days after the last dose for vaccinated children and 45–60 days after the infection diagnosis for COVID-19 recovered children. Anti-RBD IgG and ACE2-RBD inhibition were assessed by ELISA; IgA, cytokines, and cytotoxic-related proteins were determined by multiplex assays. Total B and T cell subpopulations and IFN-γ release were measured by multiparametric flow cytometry using a large panel of antibodies after in vitro stimulation with S1 peptides. (3) Results: Significant higher levels of specific anti-RBD IgG and IgA and ACE2-RBD inhibition capacity were found in vaccinated children in comparison to COVID-19 recovered children. Th1-like and Th2-like CD4+ T cells were also significantly higher in vaccinated subjects. IFN-γ secretion was higher in central memory CD4+ T cells of COVID-19 recovered children, but no differences between both groups were found in the CD4+ and CD8+ T cell effector, terminal effector, and naïve T cell subpopulations. In contrast to low levels of IL-4, high levels of IL-2, IL-6, IFN-γ, and IL-10 suggest a predominant Th1 cell polarization. Cytotoxic-related proteins granzyme A and B, perforin, and granulin were also found in the supernatant after S1 stimulation in both vaccinated and recovered children. (4) Conclusions: Vaccination with the heterologous scheme of SOBERANA® 02/SOBERANA® Plus induces a stronger antibody and cellular immune response compared to natural infections in young children.