iOS 7 has a neat new feature called AirDrop that lets you transfer files from one phone to another via Wi-Fi Direct. However, you still have to use software to identify the phone you want to share files with. On Android devices, NFC chips allow you to send files with just a tap, using Android Beam or third-party transfer software like Samsung's S Beam.
In addition, having NFC allows Android phones to participate in tap-to-pay programs, tap to enable audio on NFC-enabled stereos and headphones, and tap to get information at NFC-enabled kiosks. Still no sign of NFC from Apple.