I've not been one to complain of lag or frame drop, but iOS v11.0.x and 11.1.0(b1-3) were just horrid. I would press the home button on a 6S+ or iPad Pro and nothing would happen -- at all -- often. This wasn't lag, it was unresponsive and messed up to locked up. A few times it would take a hard reset.
I have tried to pin it to system processes sucking too much CPU, or spinning it horribly, as well as the App Store/Update App sucking the life out of the phone/iPad during downloads and app updates. It may be I've had iOS and Apple iCloud services going back a long ways, as well as a more complete ecosystem hitting them (phone, watch, iPad, MBP).
So ...
iOS 11.1 b4 helped a bit and 11.1 b5 helped a lot more. I expect the performance and battery issues are one and the same and the culprit, which doesn't show up on the battery usage, is system services. It looks like 11.1 is shaping up to greatly improve things. I'm not saying we'll get to where 10.3.x was, but iOS 11 is getting ready for prime time, IMHO.
Now I haven't had instant hotspot work on my iPad since upgrading to iOS 11 (works from MBP). I have many other bugs, but at least things are starting to calm down a bit.
If another beta could make as much improvement as b4 to b5, I'm for it. It's not the size of the update, if they fix some system service spin issues, or if it's a firmware patch, whatever it is, it's working.