Single Secret Leader Elections have recently been proposed as an improved leader election mechanism for proof-of-stake (PoS) blockchains. However, the security gain they provide has not been quantified. In this work, we present a comparison of PoS longest-chain protocols that are based on Single Secret Leader Elections (SSLE) - that elect exactly one leader per round - versus those based on Probabilistic Leader Elections (PLE) - where one leader is elected on expectation. Our analysis shows that when considering the private attack - the worst attack on longest-chain protocols - the security gained from using SSLE is substantial: the settlement time is decreased by roughly 25% for a 33% or 25% adversary. Furthermore, when considering grinding attacks, we find that the security threshold is increased by 10% (from 0.26 in the PLE case to 0.36 inthe SSLE case) and the settlement time is decreased by roughly 70% for a 20% adversary in the SSLE case.