Nick Cave is VERY eclectic. The Birthday Party were a very off-kilter, deranged, sleazy and more than slightly crazy post-punk band. Then he started his own band. It started off being like evil, dark and raw blues, and slowly developed in sound. He was able to write some great ballads, in all senses (story songs, and slow, soft songs). A fascination with grim folk tales, and a great lyrical touch really sets him apart from most of his peers.
For an indication of the way his sound has developed, here's a few examples:
http://www.youtube.com/watch?v=l5I2vEcVC_I&feature=related
The Birthday Party "Nick The Stripper", 1981 - sleazy, dark, sinister.
http://www.youtube.com/watch?v=-OccHxBWcE4
Nick Cave and the Bad Seeds "Your Funeral, My Trial", ca.1985 - balladeering, murderous, wistful, folk-tinged.
http://www.youtube.com/watch?v=Ahr4KFl79WI
Nick Cave and the Bad Seeds "The Mercy Seat", 1988 - epic, driving, pulsating song about a condemned man.
http://www.youtube.com/watch?v=thHx7cdoaAc
Nick Cave and the Bad Seeds "Weeping Song", 1990 - evil cabaret.
http://www.youtube.com/watch?v=lDpnjE1LUvE
Nick Cave and Kylie Minogue "Where The Wild Roses Grow", 1996 - romantic yet sinister duet between corpse and killer.
http://www.youtube.com/watch?v=WuDP7c3Zd8I
Grinderman "No Pussy Blues", 2007 - furious, tense, angry blues-rocking.
What makes Nick Cave great is that he manages to combine music from all kinds of deadbeat, outsider groups; he sings the stories of prisoners, carnies, criminals and drunks; he is able to combine having the founder member of German industrial noise-terrorists Einstürzende Neubauten alongside a member of atmospheric Australian instrumental balladeers Dirty Three in his band; he stays true to the music of the past with blues, ballad and folk inflections, yet creates something unflinchingly modern and uncompromising. Always dark, usually sinister, he always seems to want to hark back to the days when Australia was a wild and dangerous place (as seen in his film The Proposition). And he's a brilliant lyricist who's willing to push the boundaries of what's acceptable (his cover of Stagger Lee turns the card-playing, gun-toting baddie into an unrepentant, womanising monster forcing people to perform unspeakable acts at gunpoint), ties things down with black humour, you can always imagine him with a sick, evil grin on his face.
I know quite a few Aussie bands. Some I like, like Dead Can Dance, the Triffids (or are they kiwis? I think they're Aussies), others I don't.