NadHAT v1 is available in two versions, what are the differences?  
Without any distinction, both NadHAT v1 boards allow the sending/receiving of data according to different protocols on the 2G/GPRS mobile network. This data can be exchanged as a SMS or MMS (size <300Ko), but also according to the HTTP, FTP, STMP protocols.  
In addition to all GSM/GPRS features, the BT version allows to:
- Pair the SIM800C module to a BT headset, and thus pick up/hang up an incoming audio call (wearable application)
- Establish a wireless serial link between the module and a third-party device for data exchange, including a pi card without a wireless interface.  
Which version of the NadHAT board should I choose?  
If you want to use the NadHAT board with a Raspberry PI 3 or Zero W board, know that the version without Bluetooth is recommended. There is no protocol for coexistence between the Cypress CYW43438 chip on the Raspberry PI 3 or Zero W board and the Mediatek MT6 chip 261 of the SIM800 module on the NadHAT board. It is therefore not possible to use the NadHAT Bluetooth connection simultaneously with a Wi-Fi connection with the Raspberry pi board. It will only work badly or very badly.
On the other hand, on a very inexpensive PI Zero v1.3 board, or a Raspberry Pi A/B+/2 without a wireless radio chip, the bluetooth option can be interesting in order to be able to exchange data wirelessly with a nearby device. Another possible use case in the field of "wearable" is the possibility to use a Bluetooth compatible headset to receive an audio call by a simple pairing.
Note that the antenna does not come with the BT version. However the Bluetooth works at the same frequency as the Wifi, ie 2.45GHz. Antennas with a U.FL/IPEX connectivity are very common.