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Both campaigns are EXACTLY the same, same keywords, same PPC costs, etc - Exact.
The only difference is that the display ads are totally different as are the display URL and the Destination URL and the daily budget is different.
siteA.com is a campaign that has been running since 12/04
siteB.com is a campaign that is new.
When I start the campaign for siteB.com you no longer see the ads for siteA.com.
They should not be competing with each other as destination URLs and display URLs are totally different.