To not drain the battery heavily you need Bluetooth Smart / LE (Bluetooth 4) support in both the Garmin device and the phone.
Windows phone is fine so long as it has Win 10 and the phone itself supports Bluetooth 4.
Same goes with Android (4.3 and above and BT4)
And iPhone just needs to be the latest OS.
http://www.garmin.com/en-GB/ble
As for moving to Android, my experience has been poor efficiency with the battery, though latest versions may be improving. It’s hard to judge as many Android devices just solve the problem with a massive battery making the phone huge. Win Phone and especially on Lumia devices I’ve found has been far better. Though I’m reluctantly probably forced back to Android for next phone given the poor state of Win Phone now. Got my eye on a Nokia 6. Sure it’s not the old Nokia and parts are made in far east, but the company is made up of ex Nokia staff. The hope is build quality and battery life will be true to Nokia standards of old.
p.s. I’ve also found my Garmin 510 to be a nightmare to pair with phones. Both Android and Win Phone.