For example, Google Adplanner calculates its unique visitors using Cookies over a specific month. If users delete there browser cookies, you can see it will shower higher.

If you look where Complete gets its information from, they say:
“Compete applies a rigorous normalization methodology, leveraging scientific multi-dimensional scaling to ensure metrics are representative of the U.S. Internet population. Compete members are recruited through multiple sources to ensure a diverse distribution of user types and to facilitate de-biasing across the data sources. Compete’s standard normalization process is applied to our monthly and weekly metrics. Compete relies on share based measures to report its daily metrics.”
which again, is complete different from Adplanner.

You also have to make sure that you when your comparing data, you are comparing US to US, not US to Everything.

I hope this answers your questions to why the results are different.

Sincerely,
Alexander

- J.
Web Designing