Well, I'd say they both provide very solid and valid views over the same problems.
When used together, the power of both approach is amplified.
A very interesting approach to dig here.
COBIT: Released as an IT process and control framework linking IT to business requirements, COBIT initially was used mainly by the assurance community in conjunction with business and IT process owners. With the addition of management guidelines in 2000, COBIT was used more frequently as a management framework, providing management tools, such as metrics and maturity models, to complement the control framework. With the release of COBIT 4.0 in 2005, it became a more complete IT governance framework. Incremental updates to COBIT 4.0 were made in 2007; they can be seen as a fine-tuning of the framework, not fundamental changes. The current version is COBIT 4.1.
ITIL v3: Released by the UK Office of Government Commerce (OGC), ITIL it is the most widely accepted approach to IT service management in the world. Version 3 consists of 27 detailed processes organized into five high-level processes described in five core books—Service Strategy, Service Design, Service Transition, Service Operation and Continual Service Improvement—that comprise one function: effective IT service management. In addition, ITIL v3 introduced the concept of the service life cycle and this is described in the book Official Introduction to the IT Service Lifecycle.
The mapping is performed in two layers. A high-level mapping compares the components of ITIL V3 with the components of COBIT and shows the coverage of IT governance focus areas.
