My initial message was more meanth as a neutral message and as remark on the message that the Iphone 6.0 with BT 4.0 connects . than as a question. I use my Mi band 3 mostly on a Galaxy Note 4 and that works more or less (about the less later) Of course over Bluetooth because thats the only way to connect to the MiFit app. The Galaxy S4 mini is used as a "Sports-phone" because of the small size. Would be nice when my Miband also runs on the S4 but not a must because all i need is on it (Very accurate HR over chest-strap, GPS, my favorite running music and the super-app Runtastic)
About the less; My Galaxy Note 4 (Android 6.01, BT 4.1) sometimes looses Bluetooth connection with the band and there is no automatic reconnection . Tried stop/start BT, un-pair / re-pair the band, clear cache of BT-apps but nothing helps. The only thing that helps is restarting the Phone.
P.S. Also booting in Recoverymode and clear the total cache helps for some time but after a while the problem continues