What's wrong with "psychological horror"? That does the same job in terms of genre description. "Elevated horror" is snooty, pretentious, and condescending for all the reasons I outline.
As to whether you're in for high calibre or shlock, that can be assessed from director/screenwriter and so forth. A Stanley Kubrick science fiction film (2001: A Space Odyssey) isn't ever referred to as "elevated" science fiction, but his name carries clout, enabling the viewer to distinguish between his film and the many other less serious sci-fi films exploring AI, the meaning of life, etc.