I like the westerns too, but in regards to Italian horror, I'm attracted to them mostly for their look (they're always beautifully shot on luscious locations, and have great art direction) and their sound - they have great soundtracks by Morricone, Cipriani, Rustichelli, Donaggio, and Simonetti/Goblin.
They're on a thin line between art and sleaze. They look artful, but the content is often sleazy: they have immoral characters, lots of sex and nudity, the killer is nearly always referred to as a sex maniac
I love the Gothic and giallo (thriller) pictures from the sixties and seventies mostly. Castle of Blood from 1964 is one of the greatest black/white Gothic films, it has an hypnotic quality.
In comparison with American and British horror they have a more dreamlike quality (although the Hammer films from the fifties and sixties come sometimes close to a similar feel) which is typically Italian - you also find it in Italian comics like Dylan Dog. The mood and atmosphere comes completely before any logic. They can however be slow to modern tastes, but you can get used to that. I think musicvideos have influenced film a lot in the eighties, before the eighties movies and tv were generally slower. Although the unfocussed screenplays of Italian films can make them too directionless for some - they can go wildly from one thing to another, introduce new characters halfway the film, or go into quite unrelated events. So, it's not for everybody.
And there is the dubbing that puts many people off: as a rule they all got dubbed either in English or Italian. They don't use onset sound. Many blu-rays now have the option to listen to English as well as Italian. I always choose the latter, because I find the dubbing less obvious in Italian.