Hi,
That sounds like a definite candidate for duplicate content issues. A true responsive design only has one set of page elements coded, which then rearrange based on screen size, that's what makes responsive the optimal solution for SEO. Search engines only have to read one code set per page and they know it'll render for most devices. In your case, I believe search engines will view that as a tactic to game the system; one version of the content is essentially cloaked when the other is displayed.