IPhones don't make better photos. They have a decent camera (as far as phone cameras go) but there are other phones with better cameras. There are tons of options for post-processing on both Android, Windows Phone and iOS that are better than the built in camera apps on any of the phones. Adobe even makes a mobile version of "Photoshop" though it's really nothing at all like Photoshop.
As far as recommendations of specific mobile applications, I don't do much in the way of processing on my phone as I have yet to find any phone based software that works as well as using a PC. The Photoshop app might be worth a try, though there are probably better options available cheaper. I'd recommend looking in the app market for well rated apps that are compatible with your phone.