Sounds like a hardware fault to me. Yes, there are a few efficiency issues with the 8.1 dev preview which have largely been solved with the latest update. At no point, however, have there been significant slowdowns or major battery drain. It is particularly telling that you had the same prob with 8.
Try hard reset of course, and if particular apps are causing this don't install them. Then test. If you still have the same issues go back to 8.0 and test again, if still an issue contact Nokia Care as a hardware fault sounds likely.