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Best answer has been provided by Vinod Jeba Azir for the comprehensive comparison. The other published answers are also great and must read.

Prior to comparing RAPID and DACI matrices with RACI matrix, let us briefly understand what an RACI matrix is. RACI is a short form for Responsible, Accountable, Consulted and Informed. It is a tool quiet extensively used in project management to define individuals’ roles and responsibilities in the execution of projects while removing ambiguities and provides clarity to all stakeholders. This topic is discussed in detail in the “benchmark six sigma forum” and can be accessed using this link. What is RAPID matrix? RAPID is short for Recommend, Agree, Perform, Input and Decide. It is yet another tool used in project management. While RACI matrix is used to define high level roles and responsibilities, RAPID matrix is used to define more lower-level project planning and decision-making responsibilities. RAPID matrix example What is DACI matrix? A DACI matrix, expanded as Driver, Approver, Contributor and Informed is also a tool used in project management to define / identify key roles and responsibilities for making group decisions for every major task within a project. DACI matrix example Comparison between RACI, RAPID and DACI matrices: Matrix RACI RAPID DACI Expanded as Responsible, Accountable, Consulted, Informed Recommend, Agree, Perform, Input, Decide Driver, Approver, Contributor, Informer Year 1970 After 1980 1980 Founders Kristoffer Grude, Tor Haug and Erling Andersen Bain & Company Intuit Application Tool used to clarify & define roles & responsibilities to people within a project / team. Tool used to agree and assign decision making roles and accountabilities. A variant of RACI used to assign roles to personnel who drive projects to conclusion. Merits þ Well known and used throughout organizations þ Once you assign the ‘A’ person, leave it to the team to make it work þ Preferred by 3rd party companies (e.g. consulting companies) as it has a specific person (A role) to deal with þ Enforce a recommendation or a decision, which is typically the blocker þ Role allocation is clear to manage the activities from beginning to end (entire lifecycle) þ Preferred by teams that want to get things done þ Eliminates ambiguities by giving full authority over definite aspects of decision making to a specific person þ Representing every aspect of decision-making with a specific role þ Removes collective responsibility and corrects team imbalance by giving authority to a single person / role þ Eliminate probable disagreements and speeds up decision-making Demerits ý Everything is dependent on ‘A’ role ý No strong focus on teamwork ý Confusion may arise between Consult / Inform roles & Responsible / Accountable roles ý May lead to shortcut and not well-thought through options ý Not easy to implement as everything is not just link to one person ý Trademark limits use due to legal concerns ý Model only works if the rest of the team members are prepared to accept the decision made by the approver