Atv3 or iphone 5 with lightning av adapter

[cherrypik]

I'm looking for opinions on either one of these setups. I currently have a iphone 5 and ipad3 and wanted to airplay to my hdtv. Can I just purchased and hook up the lightning av adapter to the iphone 5 and it will work like the ATV3? What advantages does the atv3 have over the iphone 5? I really don't purchase movies from itunes and will most likely airplay them from my computer through my phone to the hdtv or slingbox it from my other tv.