I had the same question from Marketing two months ago. What I found out is this: Adwords attributes Conversion to, as they say, Last Adwords Click. So Adwords gets the conversion if it was in the conversion path. First, second, no matter where. If it was in there, AdWords takes the credit. In Omniture it probably is a last click attribution, depending on which conversion variable you're using and how your report(s) are set up,
From what I've read on Google Support AdWords cookies standard expire after 90 days. So any AdWords click within a period of 90 days gets the conversion. No wonder you see AdWords demand 4 times as high as in a (more realistic) Last Click attribution model, with a (more realistic) cookie lifetime.
Best,
-Harry