I am skeptical that 6.1 is going to fix these battery issues. Apple had already made the claim of "same battery life as S4" when testing the watch with OS 6.0. Why does everyone seem to think that OS 6.1 is going to meet that claim when it is finally released?
Case in point: Apple claimed major battery life improvements on the iPhone Max Pro. This is absolutely true and it was true even with the mess that 13.0 was. Apple made these claims for the OS the watch was running on, not the OS that is coming at some point down the road. iOS 13 has been a very buggy release (hence the massive amount of updates we have seen). One thing that was true on day 1 was the stellar battery life regardless of the mess the rest of the OS has been for some people. I don't know why people assume the same wouldn't hold true for the watch. Apple tested the watch on 6.0 and made the claim of battery life based on 6.0.
I just don't think that there is going to be a major fix for this until Series 6 comes out next year with a more efficient processor. There could be marginal improvements for sure with OS updates but not anything major like people are expecting. I think Apple took a pretty big shortcut this year by not giving an update to the processor and I think its going to hamper the battery no matter what they do, unless you turn off the AOD. I hope I'm wrong and I guess we'll see soon enough.