Whether analyzing the CMM or CMMI, there is one thing shared by both works that makes them unique, they are models, not standards, for improving product quality and process performance. (Source: http://resources.sei.cmu.edu/asset_files/TechnicalNote/2008_004_001_14924.pdf)
The most experts mean that agile development and CMMI can coexist. It depends normally on the CMMI level which is used. The agile manifesto is nearly incompatible with levels 4 or 5 from CMMI. (Cf.: http://www.ciodashboard.com/it-processes-and-methodologies/agile-cmmi-compatible/) CMMI is divided into five different levels.
This text is written to give you a short overview in which kind of dimensions CMMI and agile developments can be compared and in which they are incompatible.
Capability Maturity Model® Integration (CMMI) is a process improvement approach that provides organizations with the essential elements of effective processes. (Source: https://www.scrumalliance.org/community/articles/2008/july/agile-and-cmmi-better-together)
In agile development the focus is on evolving systems in short iterations. The output from each iteration is a running system. The following list give a short overview about some agile methods: (Cf.: http://www.sei.cmu.edu/library/assets/dutton.pdf)
In the following phrases a few dimensions from CMMI Paradigm are compared with a possible match with agile developments.
This CMMI dimension can be good integrated into agile developments. But the project plan would be more detailed to begin of each iteration. Before the agile iterations could start an initial release plan must be created. Especially the risk management is more detailed. CMMI can reduce the risk in agile development projects.
This CMMI dimension has although a good match to agile developments. The goal from both methodic are the same. But the Change Management Audits from this CMMI dimension are not compatible. Agile developments want automated controls. In this case the operator has to decide for one site.
In CMMI the focus is not set on the Team. The focus is located on the project itself and the organization. Agile development is Team focused. Each Team member has normally their own project task. That could be an issues if CMMI are implemented into running development Team.
CMMI and agile development are different kind of methodic. It can good compare to a level 3 in CMMI. CMMI and agile development both add a huge value to projects. In some cases, the project manager has to decide to drift deeper into one of these two methodic. In some organizations it could be not possible to compare CMMI and agile development.