Maybe a bit delayed, but technologies have evolved since so there is certainly new info around which draws fresh light on the matter...
As iOS has yet to open up an API for WiFi Direct and Multipeer Connectivity is iOS only, I believe the best way to approach this is to use BLE, which is supported by both platforms (some better than others).
On iOS a device can act both as a BLE Central and BLE Peripheral at the same time, on Android the situation is more complex as not all devices support the BLE Peripheral state. Also the Android BLE stack is very unstable (to date).
If your use case is feature driven, I would suggest to look at Frameworks and Libraries that can achieve cross platform communication for you, without you needing to build it up from scratch.
For example: http://p2pkit.io or google nearby
Disclaimer: I work for Uepaa, developing p2pkit.io for Android and iOS.