Samsung has updated its Gear Manager Android application to version 2.1.14052101. There is no change log available presently, but there are no obvious feature improvements at this point, however in early test battery life does seem to be a little better overall on the Samsung Gear 2.
I found there was no update notification for the application, and you had to manually go into Samsung Apps Store to query for an update. whilst updating the Samsung Note 3, I did get stuck at 22% update, when it was updating the software on the Gear 2, and a reboot of both the Smart phone and Smart watch seemed resolve the situation.
How as your update experience been? Please let us know in the comments.