It happened a lot with Fulci and Argento. The original release here of
Phenomena (as
Creepers) was simply horrific (no pun intended); and lacked all the subtleties of the full film while retaining all its vices.
Suspiria didn't suffer as badly, but was still not, as I recall, as coherent as it might have been, and so forth. I've still to see a restored version of
Profondo rosso, so don't know about that, but suspect the same would apply there.
Luci suffered even more from this, given that his violence and gore were even more extreme. Oddly, though, it was often as much -- or more -- the scenes which contributed to the actual plot or character development which ended up being excised as was the gore.
Paura nella città dei morti viventi (
City of the Living Dead) is a seriously flawed film from the get-go, but at least it is somewhat better in the restored version, while
Quella villa accanto al cimitero (
The House by the Cemetery) is at times almost unwatchable as a story (though if you're into it for the gore, as with pornography being into it simply for the sex scenes), then perhaps all the better; yet it, too, makes more sense and develops an atmosphere of creeping menace when seen in its restored version. In each case, the gore generally becomes at least more logical -- in a weird, horrific fashion -- with the restorations, rather than simply having no more point than to titillate.
And, of course, several of Fulci's films develop his theme of the Gates of Hell and their opening into our world, often having a tinge of Lovecraftian angst or the exoticism of Clark Ashton Smith, to whom he gives nods in some of them. I think that is what drew me to Fulci, really; the development of this theme seems to hint at more than what we see on the surface.
Incidentally, I recently came across an interview with Fulci which allows some interesting insights into these films, with especial reference to
House by the Cemetery and its ending:
http://www.shockingimages.com/fulci/interview2.html