ITIL V3 gained popularity from the then newly introduced concept of managing IT Service Management Life-cycle. They saw it as a complete picture and a roadmap to achieving IT business maturity. The framework handed out 5 core books each in-depth, explaining life-cycle stages within IT Services right from the conception stage to recurring improvement and finally a exit to retirement.
The V3 framework picture looked perfect in view of all those who wanted to have more of ITIL from V2 where it was mostly Service Delivery and Service Operations. The version of ITIL V3 has Service Strategy, Service Design, Service Transition, Service Operation and Continual Service Improvement phases that touched upon (debatable) 27 processes covering the stream
While most of the ITIL adopters focused on improvisation of processes within the Infra, Ops and the transition between Dev and Ops, the others tried implementation of processes from the Design phase as well. The point is the framework appeared complete but nevertheless it was highly difficult to have it all implemented and there were many reasons for it (Some of them are discussed on forums and probably triggered the development of ITIL4).
ITIL4 has a different view altogether on life-cycle. Although there is no specific mention of life-cycle phases or any new introductions to the life-cycle approach, it does have reference to means of conceiving, designing, transitioning, operationalizing, internalizing or whatever it takes to mature the services around IT.
The significant drawback of Life-cycle model was that it projected a perception of serial, one-way approach to IT Service Management. This has been handled in ITIL4 by removing the reference to life-cycle stream and allowing the organization to follow Value Stream Mapping and Service Value Chain methodology.
Try out the interactive picture to understand Value chain interrelations