Dificulty > Complex
Simple methods are easy to use (for example), require shorter period of time (eg. Bodymaping), and use a small amount of material (Path to Participation). However, you can collect lots of information (Questionnaire, Communication Mapping), develop a lot of ideas (Brainstorming, Six Thinking Hats), discuss your ideas (Focus Groups) select ideas with potential (Affinity Diagram) or on a simple way present your service (Lego Serious Play, Prototyping) or verify your service with potential users (Service Prototype).
On other hand, Complex methods require extra preparation before actual release; then, very often more people has to be involved or require a lot of different materials to be used or method delivery require longer period (User Diaries, Service Safari). However, with these methods you will be ale to collect richer data about the user (Video Ethnography, Day in a life, Empathy Tools) get more detail understanding service process (Actors Map, Process Analysis, System Map), relationships between people involved in service design (User Journey) or verify your new proposed service (Experience Survey, Offering Map).