Both are offer a step-by-step approach for teachers (or instructional designers) to follow, both have same overarching principles, using materials and evaluate the learners.
Difference
Analysis step of ASSURE focuses on the learner, rather than the ADDIE analysis which focuses on the scope of the instruction and their needs.
ADDIE model focuses on modes of presentation, or how the material will be presented, while ASSURE allows for slightly modified the materials to accommodate the instruction.
The ASSURE model has a specific step to insure the participation of the learner, but ASSURE does not include a step where that is a focus of the instructional design model.
I prefer ASSURE model because it reinforce that learners are actively engaged not passive
