From what I can tell, claims that the Amazon Appstore is cheaper than the Android Market seem overblown. Looking through both stores, I don't see any major discrepancies on popular apps. However, Amazon has vowed to give away a free app every day, starting with Angry Birds Rio. The Android Market offers no deal promotions whatsoever.
Advantage: Amazon Appstore
The Web interface for Amazon's Appstore is tied into the rest of the retail site, which means if you search for the Evernote app, you'll also see results for "iPad Made Simple" on paperback and other non-app detritus. I find this distracting. You also can't install apps remotely from Amazon's Website; you can only send them to a queue in the phone for later installation.
Advantage: Android Market
I'm not going to categorically declare one store better than the other, but I do think that if you're in the mood to browse--be it for deals or popular apps--the Amazon Appstore provides a cleaner experience than the Android Market. Still, the Android Market's superior return policy, bigger selection, and easier installation make it worth using if you're looking for something specific.