So here's the deal. I've always had a very bad impression of her Rainbow vocals. It was an era of excessive lipping and the parts she did sing live, most of the time, sounded really strained and cracked.
BUT, i stumbled upon this. This is actually compltely live (yes, surprising for Rainbow era!)
She dodged a lot of high notes (especially in My All, Dreamlover, VOL), and opted for ad-libs which were pretty characteristic (she doesn't do them much nowadays). I felt that the Rainbow era was behind the E=MC^2 and MOAIA eras in terms of her live vocals.