Duplicate Content in the same site is not a huge deal (ref,
Matt Cutt's blog, earlier this year).
Duplicating content between sites *is* a big deal (same article by Matt) - because Google may prefer the "wrong" site, as much as any other reason. See Matts replies to comments to his article, about half way down the current list of responses.
However, I think
SEO is a red herring for this. Looks like the crucial issue is the PPC problem.
Landing Page Quality Scores for AdWords are *usually* easy to resolve - the MinCPC primarily affects the initial value for the bid, and is only slightly related to the AvCPC (the paid CPC). So long as the advert gets a good CTR, the MinCPC will usually decline with time. This is how major brands end up with $0.02 MinCPC (No one *starts* with $0.02 MinCPC - you start with $0.05 or $0.10 or whatever, and work it down). Very often the cause of a high MinCPC is the way that the AdGroup was built, and the precise way that the landing page URL was determined by Google. Under some circumstances, altering the order of adding adverts and keywords can affect the MinCPC. Adverts with landing pages determined using DKI can be a particularly nasty problem to resolve. The nature of Google's auction *usually* means that a high MinCPC is not well correlated with the AvCPC - IOW, a $10.00 MinCPC may result in a $0.20 AvCPC because of the other participants in the auction.
From the brief outline of the problem, I'd:
1/ avoid duplicating content on another site (that site should be poorly ranked, eventually, even if you don't use robot exclusions or other techniques to prevent spidering) - mostly for reasons of brand experience and the internal costs of running/managing both sites.
2/ not worry too much about duplicating content within the site (unless you find that poorer pages are getting the rank, in which case focusing on sitemap issues, using nofollow, noindex and robots.txt can help). Google really does seem to know that customer-oriented reasons can result in internal duplication. However, putting all the link weight behind one page will probably help.
3/ work on resolving your problems with MinCPC and AvCPC by focusing on the way in which the AdGroup is constructed, and the CTR.
More information about the PPC problems might help better diagnosis.
Cheers, JeremyC.