Is there a benefit to registering digital identification via both ORCID and ResearcherID?
These two reseacher identifications fill somewhat different purposes, beside the point that one is more open (Orcid) and one more controlled (both with regard to access and data). Below, I've highlighted the main diffences I see:

Orcid provides a way to connect many different types of "outputs" with your profile, both by manually adding information or importing from a number of databases. Beside article publications you can also add posters, presentations, software, grants etc to construct a more full representation of your output, basically a full CV. 

ResearcherID is more focused on connecting published journal articles with your profile, and this is mostly geared towards importing data from Thomson's Web of Science. However, since ResearcherID is connected to a citation database it also provides citation metrics in your profile, and in that sense overlaps with a personal Google Scholar page. Orcid does not provide this functionality (at least not yet).

Since the two identification systems contain different types of information (at least for the time being), it can make sense to use them both, and as you've noted an Orcid profile can be linked from a ResearcherID profile. In terms of visibility it is probably also useful to use both, since their user bases are likely to differ. If you do not want to support ResearcherID because it is a closed Thomson Reuters product, Orcid + a Google Scholar citations page would provide basically the same information (but based on a different citation database), but with the drawback of two separate pages/profiles. I can also imagine that used exclusively, ResearcherID will probably be more useful for researchers from STEM fields compared to researchers in the humanities and social sciences, since the cover in Web of Science is known to be poorer in the latter fields.