I haven't used the Band 2 with my old Lumia 920. I've noticed that with my 640 XL, sometimes the phone call alert doesn't come through my Band until I've already answered or missed the call. It could possibly be an issue with slow communication, but that is just a guess.
Strangely, since updating to the Windows 10 preview on my phone over the weekend, I've noticed a few times where the Band pops up a new text on my wrist before the phone alerts me of the new text with sound and displaying the message in the notification bar.