Tracking outbound Google Adsense clicks
The problem is links are generated by Google. I assume Google tools does not suffice, and you can't generate report of enough quality using Google Analytics - if you could, you wouldn't ask here.

You cannot alter links. If what you display is not what Google provided, you are not getting any money. So the only sure way - generate link like http://example.org/count_ad_click/123dwe324), record click and redirect user - is closed for you.

You could cover ads with transparent link to your counting address, to avoid altering the real one. That counts as click hijacking and can hurt your reputation, badly. Browsers can start to display "possible malware" alerts, SEO position will drown and so on. Oh, and of course no money.

You still can use jQuery to append onclick to those links, and either push events to Analytics or to your own counting mechanism. Both are prone to manipulation, as they happen on a client side and user can fake those clicks all he wants, so you can get any number of false positives. On the other hand, if your reader will have javascript turned off, it will not count him at all, and some anty-hijacking plugins can prevent click count, too. Last but not least, that's the way AdSense module works now, anyway.