Despite the availability of vaccines and antivirals and the biological evolution of SARS-CoV-2, the rate of hospitalizations and deaths from COVID-19 remains high in Italy. It is crucial to understand whether and how the clinical characteristics of patients hospitalized for COVID-19 have changed over 2021–2022 and which risk factors are currently associated with adverse outcomes to develop targeted interventions. In this study, we present and compare the characteristics and outcomes of 310 patients with COVID-19 who were hospitalized between 1 August and 9 December 2021, when the Delta SARS-CoV-2 variant was prevalent (Group A), and between 3 January and 30 June 2022, when the Omicron variant was predominant (Group B). Using Survival Analysis, we estimated the cumulative 28-day hazard ratio (H.R.) of Intensive Care Unit (ICU) admission/death of patients in Group B vs. A. We built uni- and multivariate Cox regression models for the overall population and each group to identify risk factors for ICU admission/death among patient features. We found that Group B had a comparable risk of ICU admission/death (HR 1.60, 95% Confidence Interval, C.I. 1.00–2.58, p = 0.05) but a higher prevalence of elderly and co-morbid subjects than Group A. Non-invasive ventilation requirement was associated with adverse outcomes in both Group A (HR 21.03, 95% C.I. 5.34–82.80, p < 0.001) and Group B (HR 4.53, 95% C.I. 2.39–8.59, p < 0.001), as well as in the overall population (HR 3.88, 95% C.I. 2.49–6.06, p < 0.001). During the Omicron wave, elderly and co-morbid subjects had the highest risk of hospitalization and poor outcomes.