After running 11.0.1 for 30 days, updating all my 3rd party apps, uninstalling Chrome, setting up iCloud, disabling Voice Control and booting into Safe Mode, my battery finally stopped the excessive draining and returned to the 4.5 to 5 hours I was getting under Catalina.
I have a Mid 2015 15" Retina MacBook Pro with a battery at 78% of capacity.
I just installed 11.1. It took about an hour with no hiccups. It turns out there was a new major update of Microsoft Office which I installed after installing 11.1. After disconnecting my power cable, there was no noticeable decrease in battery life. I am
still getting the 4.5 to 5 hours on the battery on 11.1 as I had on Catalina.
So it looks like 11.1 does not affect battery life if you've done the things like I described above. If you've been on Big Sur less than 3 weeks and haven't updated 3rd party apps, then you should expect to see the excessive battery drain continue under 11.1.
However, during the first 3 weeks after first installing 11.0.1 and before I did all the things I described above, my battery life had dropped to less than 2 hours and I was in the same boat with a host of other users reporting excessive battery drain after installing Big Sur 11.0.1.