Designing a system involves, identifying a problem; understanding its context (the bigger problem); the various components that interact in it; decomposing the problem into smaller problems, further breaking these to even smaller problems; re-framing the problem, and then creating components to solve those problems and deciding how these small components fit together to provide needed functionality/ achieve the bigger goal. In someways, system design is a means to get to the root of the problem and figure out what the problem really is. A systems approach to design is most useful for projects involving large systems, that involve many people working together over an extended period of time.
In my opinion, designing a system and designing an experience are not exclusive. An experience in some ways is how the system interacts with it’s components. The cross-interactions between the various experiences in the system define the experience of the system. The more seamless these interaction are, more magical is the experience of the system.