I guess 'intense' conveys a gamut of musical depth and feeling.
There's 'intense', as in Tori Amos' recent releases which I find are intensely awful. Then there is 'intense', such as the music from Rodan, June of 44, Rexan and the Shipping News, which alternates with temptestuous outbursts. I loved that stuff as a teenager!
However I know now that loud or heavy, or hot and heavy is far from 'intense'. Formula rock can be the blandest experience on earth, listening to those tiresomely repetitive guitar riffs and screeching castrato male vocals jabber on about cocaine or junkie death and similar mind-numbing themes.
These days, 'intense' is more likely to be Serena Maneesh or Lisa O'Piu and the ethereal world of Marissa Nadler, whose work is intensely powerful and engagingly hypnotic.
There's 'intense, such as Veda Hille's 'Spine' album, which is the most lyrically and poetically challenging experience ever to hail from a young Canadian of her generation...then there's 'intense', such as Robin Holcomb's classic albums, which are exceptionally 'acquired taste'.
When it comes to classical music, I think of Szymanowski, Shostakovich and Bartok's string quartet cycles, as well as Schubert's 14th, which is intensely emotionally to the point of transportation to another world of aural life and death.
Lately however, I've been falling in love with the intensity of Sam Phillips' profound lyrical melodies ~ deceptively simple and classic 3 minute (or less) pop music, which conveys the most unexpected insights a listener could ever dream of. Artistry like that is unique and even perhaps, harder to access, than the kind of 'intensity' of classical music, of which, orchestral hysterics are the easiest to recognises. Many Mahlerians as well as sauerkraut Wagnerian lovers will recognise this kind of emotional whooping and hollering. However black gospel roots music equally conveys the intensity in a primal and visceral way...even if it isn't something I appreciate. The southern roots music I find most intense, is the music of Sixteen Horsepower (Wovenhand) and David Eugene Edward's spine chillingly haunting version of southern spirituality. There's always something more intense about the world of music when it crosses into spirituality, beyond life and death.
When I think about it, mostly I think 'intense' is better suited as modal adjective, if such things exist :P