Patients with chronic obstructive pulmonary disease (COPD) have an increased risk of hospitalizations, strongly associated with decreased survival, yet predicting the timing of these events remains challenging and has received limited attention in the literature. In this study, we performed survival analysis to predict hospitalization and death in COPD patients using longitudinal electronic health records (EHRs), comparing statistical models, machine learning (ML), and deep learning (DL) approaches. We analyzed data from more than 150k patients from the SIDIAP database in Catalonia, Spain, from 2013 to 2017, modeling hospitalization as a first event and death as a semi-competing terminal event. Multiple models were evaluated, including Cox proportional hazards, SurvivalBoost, DeepPseudo, SurvTRACE, Dynamic Deep-Hit, and Deep Recurrent Survival Machine. Results showed that DL models utilizing recurrent architectures outperformed both ML and linear approaches in concordance and time-dependent AUC, especially for hospitalization, which proved to be the harder event to predict. This study is, to our knowledge, the first to apply deep survival analysis on longitudinal EHR data to jointly predict multiple time-to-event outcomes in COPD patients, highlighting the potential of DL approaches to capture temporal patterns and improve risk stratification.