Background/Objectives: Guillain–Barré syndrome (GBS) is a rare but serious immune-mediated neurological disorder monitored as an adverse event of special interest during the COVID-19 pandemic. This study aimed to estimate the incidence of GBS following COVID-19 vaccination and SARS-CoV-2 infection and to compare the risk by vaccine platform. Methods: We conducted a population-based retrospective cohort study using data from the Valencia Health System Integrated Database (Spain) between January 2018 and March 2022. Two cohorts were defined: individuals receiving COVID-19 vaccines (mRNA-based vaccines (BNT162b2 [Pfizer–BioNTech] and mRNA-1273 [Moderna]) or non-virus-vectored (NVV) adenoviral vector-based vaccines (ChAdOx1-S [AstraZeneca] and Ad26.COV2.S [Janssen])) and individuals with laboratory-confirmed SARS-CoV-2 infection. Incident GBS cases were identified within a predefined 42-day risk window following vaccination or infection. Incidence rates were calculated per 100,000 vaccine doses administered or SARS-CoV-2 infections. Results: Among 5,109,919 individuals, 4,270,610 received at least one COVID-19 vaccine dose and 920,643 experienced at least one SARS-CoV-2 infection. A total of 69 GBS cases occurred within 42 days following vaccination (incidence: 0.67 per 100,000 doses), whereas 21 cases occurred after infection (incidence: 2.20 per 100,000 infections). Incidence was lower after mRNA-based vaccines (0.55 per 100,000 doses) than after NVV vaccines (1.57 per 100,000 doses). Conclusions: This study confirms that GBS occurrence following vaccination is rare. The incidence is lower among individuals who received mRNA vaccines compared to those who received NVV vaccines. Moreover, GBS appears to be more frequent after a COVID-19 infection than after vaccination. These findings highlight the importance of integrating pharmacoepidemiological analyses with pharmacovigilance data to contextualize rare but serious adverse events.