DOIs are used to identified papers, presentations, datasets, programs, figures, audio files, video files, amongst other things. ORCID iDs are used to identify researchers.
Why using ORCID iDs instead of DOIs to identify researchers?
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Because I would rather be an Orc than an Object. [/joke]
More seriously: from the horse's mouth
Our members will be aware that CrossRef has been exploring the possibility of creating an “author DOI” or “contributor ID” system. In doing so, it has become clear that the issues and use-cases involved in identifying researchers span a broad collection of stakeholders including libraries, institutions, funders, publishers and, of course researchers themselves. In short, this is not primarily “a publisher problem.” As such, we believe that the ORCID approach to creating an inclusive and open organization representing all the stakeholders in the scholarly communications process represents the best chance of creating a successful contributor identification system
The main problem with using DOI to identify authors is that the DOI model dishes out DOI identifiers through registration agencies, which usually charge some fee for the assignment. The use of registration agencies is fundamental to the design and operation of the DOI scheme. The main advantage of the ORCID scheme, as indicated above by CrossRef, one of the DOI registration agencies, is its openness and inclusiveness. Obtaining an ORCID is relatively simple.
As an aside: ORCID is a subset of the ISNI and is used for identification of researchers. For more general contributors to media, the ISNI is preferred.