Amazon launched their "Appstore" (Apple suing - no surprises - for similarity to "App Store") today, although you'll only actually have any luck in the US as far as downloading an application - as here in the UK you'll be met wit a lovely pop-up telling you that it "isn't available in your region yet".
Regardless, you can still browse the selection; check out what the app has to offer, and decide whether you'll use it with Market, instead of, or ditch it before you've downloaded a single .apk.
It does prevent a bit of an issue for developers, as well as users, as there's the inevitable confusion of "which one should I be on?" - as a user, say I'm looking for a new messaging app, I now have to search the selection in two different places, probably seeing many duplicates - but not wanting to miss out on the gem of an app that happens to be on only one store. Guaranteed to be the one I don't look in.
Hopefully, developers will just sell their apps through both, and it won't be an issue. We can choose which to use based on how cool the store app itself is, features like 15min, 24hour trial periods - or Amazon's free paid app of the day.