If McCourty took less than he was offered elsewhere, then he chose NE for reasons, at least in part, that related to non-monetary considerations. That doesn't make him Mother Theresa or someone for whom money was not hugely important, but it does mean that he did not go to the highest bidder. Given his familiarity and comfort in NE, and the fact that the Patriots are positioned to be title contenders for the next few years, it's not surprising that he might have left a few dollars on the table.
And some reports have indeed said that McCourty was offered more elsewhere.
Edit: Or what Elcab said before I hit post.