This paper investigates the underexplored area of clustering multiple survival curves, with a focus on the advantages of Functional Data Analysis for analyzing survival or hazard functions to exploit their inherent continuous nature. We propose customized functional methods, particularly leveraging Functional Principal Component Analysis, and compare them with existing methods using two real datasets: the German Breast Cancer Study (GBCS) and the Lung Cancer dataset. The results show that FDA-based methods offer faster execution times and improve clustering quality overall, highlighting the potential of FDA as a more natural and efficient approach for clustering survival curves, making it a promising direction for future survival data analysis.