Edge 820 here. The Bluetooth connection to my iPhone just works every time. I'd basically given up on BT as a useful thing years ago, but now I never have to think about it, and only have to plug the device in to charge after a few rides.

Mini review: the GPS is also super quick to acquire compared to my (now bricked) 800 - but the touchscreen is awful.

I'd echo that experience - my time with a Fitbit lead me to assume it was normal for notifications to show up long after they arrived on the phone. It's clearly just something that only some manufacturers can get right.