Which is more secure stateless or stateful?

I'm curious to understand which of the two concepts, stateless or stateful, offers a higher level of security in the realm of cryptocurrency and finance. Stateless systems, by their very nature, don't maintain any information about previous states or transactions, which might lead one to believe they're inherently more secure as there's no history to be hacked into. However, does this lack of context or continuity make them more vulnerable to certain types of attacks? On the other hand, stateful systems retain information about past states and transactions, allowing for more robust verification and auditing processes. This might seem like a security advantage, but does it also introduce new vulnerabilities, such as increased attack surfaces due to the complexity of managing and securing stored data? As a professional in this field, I'm eager to gain a deeper understanding of the security implications of these two approaches and how they compare in real-world applications. Can you elaborate on the strengths and weaknesses of each, and perhaps provide some examples of how they're being used in the cryptocurrency and finance sectors?