There're tons of threads of this kind each year.
This may or may not happen to you, but as this is a beta sometimes something defenitly won't work as expected.
Wait for the next beta and hope you're issue is gone or go back to iOS 9.
I had the same thing happen. My starage was getting completely used up and would come back as well and then be full again. I reset all settings and content from the phone and restored from an iCloud back up. Fully charged the phone and my issues were resolve. Batter life is now wonderful. Hope you have the same results. Issues happened to me in one of the iOS 9 betas and same thing worked then to so it's pretty solid.
I have installed iOS 10 Public Beta 1 two days ago... and yes, it does kill the battey pretty quickly.
However, I think I know the reason ...
I can see in the Battery Usage, that the majority of battery percentage is being consumed by (Feedback [19%] at a certain time) and (Photos 14% at a certain point in time) ... and I'm not even using these two actively.
But it seems the Feedback app keeps trying to send the reports I submitted in the background, and since yesterday the 3 reports I submitted didn't leave the outbox yet !!!
Regarding the Photos app, I'm not sure if some kind of mechanism does any analysis while the phone isn't connected to power, since that what it was saying in people album. But Photos app does consume a lot of battery in the background for some reason.
Let me know if you have the same behaviour.
Beta 2 was going to fix the battery problem which was in Beta 1. What happened exactly?
B E T A. They will not fully optimize battery until closer to release. This is a preview, not for daily drivers.
I did find the Photos app seemed to be taking a lot of CPU. The phone gets warm and the battery runs down pretty quick. It's processing the photos I imagine, and I've got 15,000 of them in the cloud. So it might calm down after a while. It's important to note I don't see this as a problem at all, since it's an early version. Optimizing is something you do near the end of the process. I expect the release will be fine.