The connection between the Dolls and hair metal bands of the Eighties is pretty clear as far as style goes. I'm sure Marc Bolan and David Bowie influenced hair or "glam" metal as well.
To the question of why the Dolls are different than some of the glam rockers of the Eighties, there's a fine line in rock music between genuine feeling and pantomime. Emotion, spirit, wit can't be faked. Where that line is drawn determines your taste (to me The Smiths seemed intensely real and The Cure seemed like a chidren's puppet show gone bad). In some cases, like the Dolls, they were more about style than substance, and would freely admit it (their contemporaries, The Ramones, were another example of guys who were great because of their attitude and intangibles rather than talent alone). Even choosing style over substance isn't easy, though: as much as some songwriters stumble miserably trying to sound "deep" and emotional, other bands can't get the hang of properly doing fun.
And so to metal. Glam metal was into a strange, baroque phase in the Eighties. It had somehow progressed into insane flamboyance while losing the one thing that was completely cool about the style in the first place, which was the tweaking of gender. "Cock rock" was a phrase in vogue, and it's a great name for those bands. They made a point of offsetting their cartoonish "glamour" by constantly barraging their fans with the sort of sexuality that would have made cavemen blush. Such was the public image, anyway; Rob Halford anyone?
But the style had congealed into mere gestures. Any semblance of real emotion or vitality had vanished from the music and the images. With the Dolls you could tell that there was nowhere else for them to go (and for many years after, that was true for some of the band members). They were projecting an image, sure, but it wasn't as easy to tear it away from who they were off-stage, whereas the Eighties glam rockers borrowed from the Dolls and others in an empty ploy for marketability. Punk and New Wave had become more interesting than metal in the early Eighties, and the times were intensely stylish-- for better and *cough* for worse-- so I think many of them sought to steal their own fashion by going back to "acceptable" people like the Dolls who were, at least, loud. It was all just pop music, fodder for MTV.
Another important difference to point out was that the Dolls did it first. For someone like Morrissey, the Dolls could appear revolutionary because, in fact, they were. The band wasn't sui generis, no, but like The Sex Pistols they might as well have been. Historians can point to other bands or artists that paved the way for the Dolls, but nothing can quite account for the seismic shock that the Dolls were-- for a few people, anyway. Hair and glam metal was more easily traceable. Putting the contrast in the simplest possible terms, David Bowie said he came from Mars and looked the part. Glam metal guys said they'd just came from the Gates of Hell but looked like they'd been down at the mall rummaging for bargains, and had the price tags hanging off their wigs to prove it.
Anyway, part of the confusion stems from the difference between real heavy metal and glam rock. Iron Maiden, for instance, is real heavy metal, despite their penchant for theatricality. Tough, bruising, expertly played music containing lyrics that mixed occult imagery with streaks of hippiedom, psychedelia, and the occasional flourish of Romanticism to show they read books. To an extent, they played the game (leather, hair, pyrotechnics) but mostly they were a respectable outfit, something like a bridge between Black Sabbath and Metallica. And there are lots of good bands like Iron Maiden, bands who could be thought of as 'real' metal and not the shallow garbage which polluted the world's consciousness in the middle to late Eighties.
(On a personal note, for the record, I don't listen to heavy metal and never have by choice, but I have had enough exposure to appreciate some of it-- the lyrics are almost uniformly abysmal but anyone with ears should be able to appreciate the incredible musicianship of many of the players.)