Stream any apps including safari? Airplay

Hi everyone,
I'm going back and forth between buying an iphone 5 with apple tv or samsung galaxy s3/galaxy note 2 and samsung allshare cast hub. Essentially Ii'd like to be able to use my phone to run games and surf the internet along with with watching movies I've downloaded (which aren't usually from iTunes). So my decision here is between ios and android. I would be 100% down with ios as apple is better but I'm afraid of the restrictions that ios places on airplay. I've heard heard there are only a few apps that are compatible and you can run only itunes content.

The thing about the android phones is that they will mirror exactly what's on my phone screen to the hdtv (via allshare cast hub which is a wireless hdmi link). I know the internet browser will work and that all games and apps will be compatible with the hdmi streaming device. But the downside is that it's android and I don't trust build quality of companies like samsung.

Can anyone tell me what is restricted on airplay/iphone 5 now? I know you use to not be able to airplay safari search engine. The internet browser is the most important thing to me and I'd like to be able to stream all apps and video streaming services from my phone.

Can I stream other internet browsers as well like firefox? Will the splashtop app work with iphone 5 and airplay?

Thanks for the help!

If you have an iPhone 4S, 5, iPad 3 (not sure on 2), OSX Mountain Lion, you can mirror to an Apple TV. I have even had my iPad screen mirrored to my 65" HDTV to watch movies not using airplay.

and, um, there is no firefox for iOS. Use Chrome, Safari or another.

So, I just want to make sure I understand your response. Anything that is on your iphone 5 or newest iPods,ipads can be streamed without restriction to an apple tv? So it's mirroring my ios just like if I plugged in a macbook through hdmi? All apps and browser capabilities are there?

So any video streaming app on an iphone will work through airplay?

^^^^ Correct on all accounts. It works flawlessly.