So I did some light googling and as far as I can tell the only real difference is that they are different proprietary standards - ANT+ is Garmin and Bluetooth LE (or Bluetooth Smart) was designed to get around that, and also address the energy consumption issues that regular Bluetooth presents.

The only functional difference that I can see is that ANT+ is reported to use marginally less energy than Bluetooth LE.

https://powermetercity.com/2016/02/1...h-power-meter/
Keith Hack: Why hasn?t ANT+ been crushed by BLE
https://www.******.com/r/cycling/com...c3&sh=b48d01f5

That last link is to a red it thread. I'm not sure why BF sensors links to red it. You aren't even allowed to say "******"