Both of the named process frameworks, i.e. CMMI and ITIL focus on quality. Here are my comparison:
- CMMI standards and guidelines are free, however you should pay for ITIL documents.
- Being free, there are lots of papers and articles on CMMI. you cannot find such info on ITIL as well.
- CMMI and its parents, i.e. CMM date back to more than 25 years ago, and it has been mature in these days. But, you cannot find such history on ITIL.
- Behind CMMI, you can find CMU and DoD that are more credible compared to the one behind ITIL.
Having mentioned these items, I propose you CMMI rather than ITIL. There are lots of similar frameworks such as COBIT and TickIT that I think CMMI is more mature than them.