Main differences, Apple has VERY high standards for apps released to the app store, Google's standards aren't AS high, some 3rd-party markets (Amazon is one) are trying to improve the quality and security of apps.
I think we all used to believe that, but if you're like me, you'll find this sample of info very interesting.
Security researcher proves that Apple's security claim is not really true:
iPhone Security Flaw Shows Potential for App Store Malware | PCWorld
Apple responds by removing his developer's license rather than working with him to fix the issue.
Can you trust that the app you got is the actual app, thanks to Apple's airtight standards?
Not really.
Fake Camera+ app hits the iPhone App Store | Naked Security
And are those unique cases or is the problem real and spreading?
Real and spreading.
How Apple is losing its grip on mobile app security
How about your personal data? Which protects it better - Apple's App Store or the independent store from Cydia?
Answer: Cydia
App Store Security Flaws - Is your iPhone Protected? 2011 Study - YouTube
Google and Apple seem about tied for security - and neither is good enough.
The idea that the App Store involves higher standards and better security is simply an urban myth, but that's just my opinion.
PS on app quality -
http://androidforums.com/lounge/494401-android-more-stable-than-ios-phandroid-article.html