I've often wondered what kind of music Nirvana would be making if they were around now. Hypothetically, imagining he had left Love and refocused on the music I wonder if Grohl's Foo Fighters style would have stated to come through more. I get the impression that had he lived Cobain would likely have left Nirvana anyway and gone solo releasing critically acclaimed but commercially unloved music. I really don't see any scenario where they would have ended up down the U2 or Muse route of being high-profile stadium rockers.
I guess it really would have depended on how/if he had sorted out his problems.
From many accounts, Cobain desperately wanted to "sit at the cool table" - you know, the one with the cranky "artistes" who disapprove of almost everything - and of course he could never make it. He was too earnest, too good of a musician and eventually too successful. Even The Melvins whom he idolized threw him over. Personally, I think this had to do with insecurity and envy on the part of other musicians, but it seems this never really occured to Cobain - he even references this rejection somewhat in his suicide note.
This to me indicates a major part of Cobain's basic personality - his self-image and self-esteem were so low that he couldn't appreciate his own talent and looked for approval in places he could never get it. He also apparently suffered a bad case of imposter syndrome, much like Janis Joplin. Also, like Joplin, (IMO) much of the grit in his music came from that inner suffering.
The direction he might have taken had he lived, I think, would have been heavily dependent on how he dealt with those issues. And the drug use, of course. - but I think his mental issues drove his drug addiction anyway.
From the beginning of his fame, he seemed like the type who wouldn't be long for the world. This isn't me rewriting history, either - I remember thinking this at the time they hit it big, and it hadn't been too long before that the singer from Mother Love Bone had died from a heroin overdose, so the grunge era had a aura of death hanging over it before it even really began.
Whatever the case, I can't imagine he would have would have turned to arena rock either - if he had, it would have only been as an ironic joke. I'm not even sure how far he would have gone without the rest of Nirvana or even the support of his wife (loathed as she may have been) they did add a great deal to the music and seemed to give him a focus he might have lacked on his own.
