Admin Graphene Mobile and Graphene Mobile Neo are two different mobile themes, with different design and different features. You can choose either one of them to use as the mobile theme for your site.
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In other words, in either case am I required to rebuild a new site in a mobile version that mimics the existing Graphene desktop site I already have, or does upgrading to either Mobile option simply adopt all the existing theme options and pages of my desktop site?
You don’t have to rebuild a new site. The mobile theme will display your existing posts and pages. Aside from that, the mobile theme has its own set of option much like the Graphene theme. See the demo sites to see for yourself how it works:
